Let X and Y be independently and identically distributed random variables. Then, what is P (X...

Let X and Y be independently and identically distributed random variables. Then, what is P (X < Y )

(a) in case the common distribution of X and Y is continuous?

(b) in case P(X=i)=P(Y =i)= 1, i=1,2,···,n.

Solutions

Expert Solution

Note: I think theres a typo in part b) as it will be P(X=i)= P(Y=i) = 1/n , for i=1,2,3,...,n . Because the pmf must sum to 1.

So proceeding with that the solution to both the parts is given in the image below. Check them out>>>

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Let X and Y be two independent and identically distributed random variables with expected value 1...

Let X and Y be two independent and identically distributed random variables with expected value 1 and variance 2.56. (i) Find a non-trivial upper bound for P(|X + Y − 2| ≥ 1). 5 MARKS (ii) Now suppose that X and Y are independent and identically distributed N(1, 2.56) random variables. What is P(|X + Y − 2| ≥ 1) exactly? Briefly, state your reasoning. 2 MARKS (iii) Why is the upper bound you obtained in Part (i) so different...

Let X and Z be two independently distributed standard normal random variables and let Y=X2+Z. iShow...

Let X and Z be two independently distributed standard normal random variables and let Y=X2+Z. iShow thatE(Y|X) =X2 iiShow thatμY= 1 iiiShow thatE(XY) = 0ivShow that cov(X,Y) = 0 and thus ρX,Y= 0

A: Suppose two random variables X and Y are independent and identically distributed as standard normal....

A: Suppose two random variables X and Y are independent and identically distributed as standard normal. Specify the joint probability density function f(x, y) of X and Y. Next, suppose two random variables X and Y are independent and identically distributed as Bernoulli with parameter 1 2 . Specify the joint probability mass function f(x, y) of X and Y. B: Consider a time series realization X = [10, 15, 23, 20, 19] with a length of five-periods. Compute the...

Let ?1 , ?2 , ... , ?? be independent, identically distributed random variables with p.d.f....

Let ?1 , ?2 , ... , ?? be independent, identically distributed random variables with p.d.f. ?(?) = ???−1, 0 ≤ ? ≤ 1 . c) Show that the maximum likelihood estimator for ? is biased, and find a function of the mle that is unbiased. (Hint: Show that the random variable −ln (??) is exponential, the sum of exponentials is Gamma, and the mean of 1/X for a gamma with parameters ? and ? is 1⁄(?(? − 1)).) d)...

Let X1, X2, . . . be a sequence of independent and identically distributed random variables...

Let X1, X2, . . . be a sequence of independent and identically distributed random variables where the distribution is given by the so-called zero-truncated Poisson distribution with probability mass function; P(X = x) = λx/ (x!(eλ − 1)), x = 1, 2, 3... Let N ∼ Binomial(n, 1−e^−λ ) be another random variable that is independent of the Xi ’s. 1) Show that Y = X1 +X2 + ... + XN has a Poisson distribution with mean nλ.

Let X1 and X2 be independent identically distributed random variables with pmf p(0) = 1/4, p(1)...

Let X1 and X2 be independent identically distributed random variables with pmf p(0) = 1/4, p(1) = 1/2, p(2) = 1/4 (a) What is the probability mass function (pmf) of X1 + X2? (b) What is the probability mass function (pmf) of X(2) = max{X1, X2}? (c) What is the MGF of X1? (d) What is the MGF of X1 + X2

Let X1 and X2 be independent identically distributed random variables with pmf p(0) = 1/4, p(1)...

Let ?1. . . ?5 be identically independently distributed (iid) variables sampled from a binomial distribution...

Let ?1. . . ?5 be identically independently distributed (iid) variables sampled from a binomial distribution Bin(3,p). a) Compute the likelihood function (LF). b) Adopt the appropriate conjugate prior to the parameter p, choosing hyperparameters optionally within the support of distribution. c) Using (a) and (b), find the posterior distribution of p. d) Compute the minimum Bayesian risk estimator of p.

Let X and Y be random variables. Suppose P(X = 0, Y = 0) = .1,...

Let X and Y be random variables. Suppose P(X = 0, Y = 0) = .1, P(X = 1, Y = 0) = .3, P(X = 2, Y = 0) = .2 P(X = 0, Y = 1) = .2, P(X = 1, Y = 1) = .2, P(X = 2, Y = 1) = 0. a. Determine E(X) and E(Y ). b. Find Cov(X, Y ) c. Find Cov(2X + 3Y, Y ).

Let Xi's be independent and identically distributed Poisson random variables for 1 ≤ i ≤ n....

Let Xi's be independent and identically distributed Poisson random variables for 1 ≤ i ≤ n. Derive the distribution for the summation of Xi from 1 to n. (Without using MGF)

Subjects