The uniform distribution of a r.v.x on four integers {12,30,55,80) is f(x)=for x = 1,2,3,4. True O False
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A: In uniform distribution, each value has equal probability of occurrence.
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- 6. Let X1, X2, .., Xn, ... be a sequence of i.i.d. random variables with U[3,7] distribution. Let Mn X1++Xn. Find a number m such that M, m. a.8.Suppose that X = {4,8,12,16} and thatX 1 ={4,8} X 2 ={4,12} X 3 ={4,16} X 4 ={8,12} X 5 ={8,16} X 6 ={12,16}Find the mean of the following:a. X 1 =___ X 2 =____ X 3 =____ X 4 =____ X 5 =____ X 6 =_____Find μ _____ Find μ (x bar) ______ Find σ _____ Find σ (x bar) _____13. A continuous random variable is uniformly distributed between 200 and 220. a. What is the probability a randomly selected value will be greater than 215? b. What is the probability a randomly selected value will be less than 205? c. What is the probability a randomly selected value will be between 205 and 215? a. P(x > 215) = (Simplify your answer.) b. P(x< 205) = (Simplify your answer.) c. P(2053. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.Consider the random sum S = X₁ + X2 + ... + XN where N represents claim frequency and X₁ represents severity. Assume that X ~ NB(r = 2,3 = 3). Evaluate fo, f1, f2.Find the Banzhaf Power Distribution for [4: 3,1,1,1,1]Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.Suppose we have a set öf n values! {x1, X2, .., Xn-1, Xn} The sample mean of the above set is x. Prove that if we multiply every value by k, then the new average will be: New average= kã (Hint: Use the formula for the sample mean with the “new" set plugged in, then simplify.)Assume that the height, X, of a college woman is a normally distributed random variable with a mean of 65 inches and a standard deviation of 3 inches. Suppose that we sample the heights of 180 randomly chosen college women. Let M be the sample mean of the 180 height measurements. Let S be the sum of the 180 height measurements. All measurements are in inches. Using R and write the code out.a) What is the probability that X < 59? b) What is the probability that X > 59? c) What is the probability that all of the 180 measurements are greater than 59? d) What is the expected value of S? e) What is the standard deviation of S? f) What is the probability that S-180*65 >10? g) What is the standard deviation of S-180*65 h) What is the expected value of M? i) What is the standard deviation of M? j) What is the probability that M >65.41? k) What is the standard deviation of 180*M? l) If the probability of X > k is equal to .3, then what is k?Please help with this statistics problem. A traffic light at a certain intersection is green 45% of the time, yellow 10% of the time, and red 45% of the time. A car approaches this intersection once each day. Let X represent the number of days that pass up to and including the first time the car encounters a red light. Assume that each day represents an independent trial. A.) Find P(X=3). B.) Find P(X<=3) C.) Find ux. D.) Find 02/x.A container contains 30 green tokens, 10 blue tokens, and 3 red tokens. Two tokens are randomly selected without replacement. Compute P(F|E). E−you select a green token first F−the second token is non−green ... Question content area right Part 1 P(F|E)=enter your response here (Simplify your answer. Type an integer or a fraction.)
