XinHongTu Automatic Car Ranking TOP13 Tent F Sunscreen Cover Summer $160 XinHongTu Automatic Car Tent, Summer Sunscreen Car Cover Tent, F Automotive Exterior Accessories XinHongTu,Tent,,Summer,Automatic,Tent,,sambaisla.com,F,Car,Automotive , Exterior Accessories,$160,/ambosexual1701633.html,Car,Sunscreen,Cover XinHongTu Automatic Car Ranking TOP13 Tent F Sunscreen Cover Summer XinHongTu,Tent,,Summer,Automatic,Tent,,sambaisla.com,F,Car,Automotive , Exterior Accessories,$160,/ambosexual1701633.html,Car,Sunscreen,Cover$160 XinHongTu Automatic Car Tent, Summer Sunscreen Car Cover Tent, F Automotive Exterior Accessories

# XinHongTu Automatic Car Tent, Summer Sunscreen Car Cover Tent, F

$160 ## XinHongTu Automatic Car Tent, Summer Sunscreen Car Cover Tent, F • [Portable and easy to operate] After the suction cup is fixed, the hand can be easily unfolded and folded. Install in 30 seconds, boot in 8 seconds. The storage bag is 34.25in/87cm long and weighs 14.3lb/6.5kg, without any additional burden on your trunk. • [Multi-function] Car tent size: 13.78*7.2FT/14.76*7.55FT, suitable for cars, hatchbacks, luxury cars, small cars, etc.; please make sure that your car can be completely covered before buying. After adding the tripod, it is suitable for outdoor barbecue, picnic, fishing, etc. • [High quality material] UV resistant polyester material, good toughness glass fiber bracket, 304 steel wire anti-theft rope, strong suction TPU rubber soft sucker. • [Double-layer windproof design] There are adjustable ropes at the four corners, which are stable and adapt to different models. The tent is semi-fixedly connected with the ribs to prevent damage or bending of the ribs. When the wind reaches level 5, the button will automatically release. • [Four seasons protection] Long exposure to the sun in the car will become hot and uncomfortable. The tent will cast shadows on the entire body of the car, reducing the temperature inside the car to 35℃/95℉, keeping away from bird droppings in spring and autumn. Protects against snow, frost and ice in winter. ||| ## Product description Please note: 1. We strongly recommend that you do not use the car tent in severe weather such as strong winds, storms, hail, etc.! 2. In snowy days, only light snow can be prevented, the visible distance is above 1000 meters, and the ground snow depth is below 3cm/1.18inch. 3. For fixation, the suction cup should be kept clean and not placed at the seam. product description When the hot summer comes, you may need a UV-proof car awning to protect your car from the scorching sun. The car tent cover can also keep your car away from acid rain, bird droppings, dust or leaves in the spring and autumn. . The car tent will be your best choice. feature 1. Folding structure design: freely stretchable. 2. Anti-theft rope design: The embedded steel wire is stronger. 3. Soft rubber protection design: effectively prevent the car from scratching. 4. Fully upgraded motor: chassis upgrade switch button, automatically power off in half an hour. 5. Upgraded version of the frame connection frame: imported PC, strong toughness and not easy to aging. 6. Ring design: to ensure the stability of the bracket in motion. 7. Double suction cups are made of nitrile rubber: double suction is more powerful. occasion Taking a nap in the car while parking, camping trips, business trips and waiting. Suitable for cars, hatchbacks, luxury cars, small cars, etc. specification Expanded size: 4.2*2.1M/13.78*6.89FT, 4.5*2.3M/14.76*7.55FT Material: Oxford canvas, fiberglass bracket, plastic connector. ## XinHongTu Automatic Car Tent, Summer Sunscreen Car Cover Tent, F ## How to Prove Markov’s Inequality and Chebyshev’s Inequality ## Problem 759 (a) Let$X$be a random variable that takes only non-negative values. Prove that for any$a > 0$, $P(X \geq a) \leq \frac{E[X]}{a}.$ This inequality is called Markov’s inequality. (b) Let$X$be a random variable with finite mean$\mu$and variance$\sigma^2$. Prove that for any$a >0$, $P\left(|X – \mu| \geq a \right) \leq \frac{\sigma^2}{a^2}.$ This inequality is called Chebyshev’s inequality. Add to solve later ## How to Use the Z-table to Compute Probabilities of Non-Standard Normal Distributions ## Problem 758 Let$X\sim \mathcal{N}(\mu, \sigma)$be a normal random variable with parameter$\mu=6$and$\sigma^2=4$. Find the following probabilities using the Z-table below. (a) Find$P(X \lt 7)$. (b) Find$P(X \lt 3)$. (c) Find$P(4.5 \lt X \lt 8.5)$. Add to solve later ## Expected Value and Variance of Exponential Random Variable ## Problem 757 Let$X$be an exponential random variable with parameter$\lambda$. (a) For any positive integer$n$, prove that $E[X^n] = \frac{n}{\lambda} E[X^{n-1}].$ (b) Find the expected value of$X$. (c) Find the variance of$X$. (d) Find the standard deviation of$X$. Add to solve later ## Condition that a Function Be a Probability Density Function ## Problem 756 Let$c$be a positive real number. Suppose that$Xis a continuous random variable whose probability density function is given by \begin{align*} f(x) = \begin{cases} \frac{1}{x^3} & \text{ if } x \geq c\\ 0 & \text{ if } x < c. \end{cases} \end{align*} (a) Determine the value ofc$. (b) Find the probability$P(X> 2c)$. Add to solve later ## Conditional Probability When the Sum of Two Geometric Random Variables Are Known ## Problem 755 Let$X$and$Y$be geometric random variables with parameter$p$, with$0 \leq p \leq 1$. Assume that$X$and$Y$are independent. Let$n$be an integer greater than$1$. Let$k$be a natural number with$k\leq n$. Then prove the formula $P(X=k \mid X + Y = n) = \frac{1}{n-1}.$ Add to solve later ## Probability that Three Pieces Form a Triangle ## Problem 754 We have a stick of a unit length. Two points on the stick will be selected randomly (uniformly along the length of the stick) and independently. Then we break the stick at these two points so that we get three pieces of the stick. What is the probability that these three pieces form a triangle? KTM Grip handle 2019-2021 ## Upper Bound of the Variance When a Random Variable is Bounded ## Problem 753 Let$c$be a fixed positive number. Let$X$be a random variable that takes values only between$0$and$c$. This implies the probability$P(0 \leq X \leq c) = 1$. Then prove the next inequality about the variance$V(X)$. $V(X) \leq \frac{c^2}{4}.$ Add to solve later ## Probability that Alice Tossed a Coin Three Times If Alice and Bob Tossed Totally 7 Times ## Problem 752 Alice tossed a fair coin until a head occurred. Then Bob tossed the coin until a head occurred. Suppose that the total number of tosses for Alice and Bob was$7$. Assuming that each toss is independent of each other, what is the probability that Alice tossed the coin exactly three times? Add to solve later ## Probability of Getting Two Red Balls From the Chosen Box ## Problem 751 There are two boxes containing red and blue balls. Let us call the boxes Box A and Box B. Each box contains the same number of red and blue balls. More specifically, Box A has 5 red balls and 5 blue balls. Box B has 20 red balls and 20 blue balls. You choose one box. Then draw two balls randomly from the chosen box without replacement, that is, you will not return the first ball into the box before picking up the second ball. If you draw two balls with the same color, then you win. Otherwise, you lose. To maximize the chance of winning, which box should you pick? Add to solve later ## Coupon Collecting Problem: Find the Expectation of Boxes to Collect All Toys ## Problem 750 A box of some snacks includes one of five toys. The chances of getting any of the toys are equally likely and independent of the previous results. (a) Suppose that you buy the box until you complete all the five toys. Find the expected number of boxes that you need to buy. (b) Find the variance and the standard deviation of the event in part (a). Add to solve later ## Can a Student Pass By Randomly Answering Multiple Choice Questions? ## Problem 749 A final exam of the course Probability 101 consists of 10 multiple-choice questions. Each question has 4 possible answers and only one of them is a correct answer. To pass the course, 8 or more correct answers are necessary. Assume that a student has not studied probability at all and has no idea how to solve the questions. So the student decided to answer each questions randomly. Thus, for each of 10 questions, the student choose one of the 4 answers randomly and each choice is independent each other. (1) What is the probability that the student answered correctly only one question among the 10 questions? (2) Determine the probability that the student passes the course. (3) What is the expected value of the number of questions the student answered correctly? (4) Find the variance and standard deviation of the number of questions the student answered correctly. Add to solve later ## Given the Variance of a Bernoulli Random Variable, Find Its Expectation ## Problem 748 Suppose that$X$is a random variable with Bernoulli distribution$B_p$with probability parameter$p$. Assume that the variance$V(X) = 0.21$. We further assume that$p > 0.5$. (a) Find the probability$p$. (b) Find the expectation$E(X)$. Add to solve later ## Expectation, Variance, and Standard Deviation of Bernoulli Random Variables ## Problem 747 A random variable$Xis said to be a Bernoulli random variable if its probability mass function is given by \begin{align*} P(X=0) &= 1-p\\ P(X=1) & = p \end{align*} for some real number0 \leq p \leq 1$. (1) Find the expectation of the Bernoulli random variable$X$with probability$p$. (2) Find the variance of$X$. (3) Find the standard deviation of$X$. Add to solve later ## Probability that Alice Wins n Games Before Bob Wins m Games ## Problem 746 Alice and Bob play some game against each other. The probability that Alice wins one game is$p$. Assume that each game is independent. If Alice wins$n$games before Bob wins$m$games, then Alice becomes the champion of the game. What is the probability that Alice becomes the champion. Add to solve later ## Probabilities of An Infinite Sequence of Die Rolling ## Problem 745 Consider an infinite series of events of rolling a fair six-sided die. Assume that each event is independent of each other. For each of the below, determine its probability. (1) At least one die lands on the face 5 in the first$n$rolls. (2) Exactly$k$dice land on the face 5 in the first$n \geq k$rolls. (3) Every die roll results in the face 5. Add to solve later ## Interchangeability of Limits and Probability of Increasing or Decreasing Sequence of Events ## Problem 744 A sequence of events$\{E_n\}_{n \geq 1}$is said to be increasing if it satisfies the ascending condition $E_1 \subset E_2 \subset \cdots \subset E_n \subset \cdots.$ Also, a sequence$\{E_n\}_{n \geq 1}$is called decreasing if it satisfies the descending condition $E_1 \supset E_2 \supset \cdots \supset E_n \supset \cdots.$ When$\{E_n\}_{n \geq 1}$is an increasing sequence, we define a new event denoted by$\lim_{n \to \infty} E_n$by $\lim_{n \to \infty} E_n := \bigcup_{n=1}^{\infty} E_n.$ Also, when$\{E_n\}_{n \geq 1}$is a decreasing sequence, we define a new event denoted by$\lim_{n \to \infty} E_n$by $\lim_{n \to \infty} E_n := \bigcap_{n=1}^{\infty} E_n.$ (1) Suppose that$\{E_n\}_{n \geq 1}$is an increasing sequence of events. Then prove the equality of probabilities $\lim_{n \to \infty} P(E_n) = P\left(\lim_{n \to \infty} E_n \right).$ Hence, the limit and the probability are interchangeable. (2) Suppose that$\{E_n\}_{n \geq 1}$is a decreasing sequence of events. Then prove the equality of probabilities $\lim_{n \to \infty} P(E_n) = P\left(\lim_{n \to \infty} E_n \right).$ Add to solve later ## Linearity of Expectations E(X+Y) = E(X) + E(Y) ## Problem 743 Let$X, Y$be discrete random variables. Prove the linearity of expectations described as $E(X+Y) = E(X) + E(Y).$ Add to solve later ## Successful Probability of a Communication Network Diagram ## Problem 742 Consider the network diagram in the figure. The diagram consists of five links and each of them fails to communicate with probability$p$. Answer the following questions about this network. (1) Determine the probability that there exists at least one path from A to B where every link on the path functions without errors. Express the answer in term of$p$. (2) Assume that exactly one link has failed. In this case, what is the probability that there is a successful path from A to B, that is, each link on the path has not fail. Add to solve later ## Lower and Upper Bounds of the Probability of the Intersection of Two Events ## Problem 741 Let$A, B$be events with probabilities$P(A)=2/5$,$P(B)=5/6$, respectively. Find the best lower and upper bound of the probability$P(A \cap B)$of the intersection$A \cap B$. Namely, find real numbers$a, b$such that $a \leq P(A \cap B) \leq b$ and$P(A \cap B)$could take any values between$a$and$b$. Add to solve later ## Find the Conditional Probability About Math Exam Experiment ## Problem 740 A researcher conducted the following experiment. Students were grouped into two groups. The students in the first group had more than 6 hours of sleep and took a math exam. The students in the second group had less than 6 hours of sleep and took the same math exam. The pass rate of the first group was twice as big as the second group. Suppose that$60\%\$ of the students were in the first group. What is the probability that a randomly selected student belongs to the first group if the student passed the exam?

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