Consider a deck consisting of seven cards, marked 1, 2,…,7. Three of these cards are selected at random. Define anrv W by W 5 the sum of the resulting numbers, and computethe pmf of W. Then compute m and s2. [Hint:Consider outcomes as unordered, so that (1, 3, 7) and (3,1, 7) are not different outcomes. Then there are 35 outcomes,and they can be listed. (This type of rv actuallyarises in connection with a statistical procedure calledWilcoxon’s rank-sum test, in which there is an x sampleand a y sample and W is the sum of the ranks of the x’s inthe combined sample; see Section 15.2.)

Q: Suppose that X,Y, and Z are random variables with X ~ Bin(16, 1/4), Y ~ Geom(1/2), and Z ~…

A: Solution: Let X, Y and Z are random variables.  X~B(n= 16, p=1/4)Y~Geom(p=1/2=0.5)and Z~Poisson(λ=5)…

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Q: Let X € {0, 1} and Y E {0, 1} be two independent binary random variables. If P(X = 0) = 0.3 and P(Y…

A: Given: P(X = 0) = 0.3 P (Y = 0) = 0.8 X and Y are independent

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Q: Suppose T and Z are random variables.   a. If P(T>2.19)=0.11 and P(T2.05)=P(Z2.05).

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Q: Suppose that we have a sample space with six equally likely experimental outcomes: x1, x2, x3, x4,…

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Q: Let X € {0, 1} and Y E {0,1} be two independent binary random variables. If P(X = 0) = 0.2 and P(Y =…

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Q: Suppose T and Z are random variables. a. If P(T> 2.98) = 0.03 and P(T0.53) = P(Z0.53) a. P(-2.98…

A: a. It is given that, P(T > 2.98)= 0.03 That is, P(T ≤ 2.98)= 1- 0.03              P(T ≤ 2.98)=…

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Q: Generate the first five random numbers (0 to 1) using Linear Congruential method. Given: a = 7, c =…

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Q: Exercise 9. Suppose that Z,, Z2,Z3 are independent N(0,1) random variables. (c) Compute P(Z? + Z3 +…

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Q: If X, Y, Z, and W are random variables, then show tha (a) Cov(X + Y, Z) = Cov(X, Z) ± Cov(Y, Z). tud

A: Given that, If X, Y, Z, and W are random variables.

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Q: Let X € {0, 1) and Y E (0, 1} be two independent binary random variables. If P(X = 0) = 0.3 and P(Y…

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Q: 4. Show that if X and Y are independent random variables, then E(9(X)| X = ro) = g(ro). %3D

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A: Given that P(X = 0) = 0.2, then P(X = 1) = 1 - 0.2 = 0.8 P(Y = 0) = 0.8, then P(Y = 1) = 1 - 0.8 =…

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Q: (a)  P(x≤1),n=5,p=0.4 P(x≤1)=  (b)  P(x>3),n=9,p=0.7 P(x>3)= (c)  P(x<7),n=8,p=0.6 P(x<7)=…

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Q: Suppose that X, Y, and Z are random variables with X~ Bin(16, 1/4), Y ~ Geom(1/2), and Z ~…

A:

Q: Suppose T and Z are random variables. a. If P(T> 2.98)= 0.03 and P(T0.53) = P(Z0.53). a.…

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Q: Let X and Y be two discrete random variables with the joint probab given by: f(x,y) 0 1 2 0 1/6 1/3…

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Q: Suppose T and Z are random variables. a. If P(T> 2.52) = 0.02 and P(T 0.36)=P(Z 0.36).

A: The provided information is…

Q: Let X € {0, 1} and Y E {0, 1} be two independent binary random variables. If P(X = 0) = 0.2 and P(Y…

A: Let, Let X  ∈ {0, 1} and Y  ∈ {0, 1} be two independent binary random variables. Let, P(X = 0) = 0.2…