Let Z be a discrete random variable with E(Z) =0. Does it necessarily follow that EC 7³ ) = 0 ? If yes give a proof; if nogice a Counter example.
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![a discrete random
Let Z be a
variable with E(Z) =0.
Does it necessarily follow that E( 7³ ) = 0 ? If
yes, give a proof
proof; if no
norgive
a
Counter example](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35bc7cfb-e38c-45d6-8cb2-8c987ddfb016%2F0fb4809b-b99e-4d40-aa45-5281f0ea282e%2Fj78oc8n_processed.jpeg&w=3840&q=75)
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- Let Xi NcO,1) and n =2 auel T=X,+ Xz Show that Tis a %3D Sufficieacy stanslic Sufficieney Statistic.a) Let X₁, X₂, X3,..., Xn be a random sample of size n from population X. Suppose that X~N(0, 1) and Y = – Σ₁=1 Xi √n - en. What is the probability that Y² is between 0.02 and 5.02?Suppose X is a random variable with E(X) = 0 and Var(X) = 2. What is E(X2 )? a). 1 b). 2 c). 3 d). 4 e). none of above
- Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" (g) and "boys" (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is bbg, then R(bbg) = 1. Suppose that the random variable X is defined in terms of R as follows: X=R- - 2R-4. The values of X are given in the table below. Outcome bbb ggb bbg gbg gbb bgg bgb gg Value of X-4 -4 -5 -4 -5 -4 -5 -1 Calculate the values of the probability distribution function of X, i.e. the function py. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X Px (x) E 1:48 PM 3/21/2022 hp Compag LAI956X 立An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is tth, then N (tth)=2. Suppose that the random variable X is defined in terms of N as follows: X=N²-2N-2. The values of X are given in the table below. Outcome ttt htt hhh tht tth hth hht thh Value of X 1 -2 -2 -2 -2 -3 -3 -3 Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P(X=x) 0 0 0 0 0 00 X ŚA particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. (Round your answers to three decimal places.) In USE SALT (a) What is the probability that at most 5 of the calls involve a fax message? (b) What is the probability that exactly 5 of the calls involve a fax message? (c) What is the probability that at least 5 of the calls involve a fax message? (d) What is the probability that more than 5 of the calls involve a fax message? You may need to use the appropriate table in the Appendix of Tables to answer this question.
- Assume that X is a hypergeometric random variable with N=50, S= 20, n=5. Calculate the following probabilities. A) P(X=2) B) P(Xgreaterthanorequalto2) C) P(Xlessthanorequalto3)I roll a die with 10 faces numbered 0-9 and obtain a score X. What is E(X)? In order to obtain a random number between 0 and 99 I roll the die twice obtaining scores X and Y, then set Z = 10X + Y (i.e., the first roll determines the "tens", the second roll the "ones"). Is it true to say that E(Z) = 10E(X) + E(Y)?4.9Q) Let P and Q be two random variables such that E(P) =7 and E(Q)= 4, then E(4P+3Q+5) is: 1)42 2)44 3)45 4)38
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