2.6.5. A discrete random variable X is such that P(X 2") n= 1,2 2" Show that...
Show all steps. Thanks. 2.6.4. A discrete random variable X is such that 2n-1 P(X = n) =-, n=1.2, . . . , n, . . . . Il Show that EX- 3. 2.6.5. A discrete random variable X is such that P(X=2") = 1 2" n=1.2, . , show that EX = oo. That is, X has no mathematical expectation.
2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a...
9.A discrete random variable X has pdf of form f(x) x-1,2, ...n, and zero otherwise. A) Find c. B) Find an expression for f (x). 10. If f(x) Cx for x 1,2,3, ... pq*-1 otherwise Find an expression for F(x). Show your work! 9.A discrete random variable X has pdf of form f(x) x-1,2, ...n, and zero otherwise. A) Find c. B) Find an expression for f (x). 10. If f(x) Cx for x 1,2,3, ... pq*-1 otherwise Find an...
Problem 3. Let X be a discrete random variable that takes values in N. Show that if X is memory-free then it must be the case that X Geo(p) for some p. (Hint a useful first step might be to show that P(X > t)= P(X > 1)' for all t E N.) Problem 3. Let X be a discrete random variable that takes values in N. Show that if X is memory-free then it must be the case that...
2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from this distribution: {2,3,10}. a. Find the method of moments estimate for 0 HINT: a very useful fact is that k1 n(n+1) 2 b. Find the MLE for 0 c. Which estimator is unbiased? d. Which estimator is preferred? 2. (Discrete uniform). Consider the PMF P(X x)= for x 1,2,...0 _ You have a random sample of size three from...
A discrete random variable A takes values {1, 2, 4} with probabilities specified as follows: P[A = 1] = 0.5, P[A = 2] = 0.3 and P [A = 4] = 0.2 Given A= ), a discrete random variable N is Poisson distributed with rate equal to 1, that is: 9 P[N = n|A = 1] = in n! el Hint If N is Poisson distributed with rate 1, its expectation and variance are as follows: E[N] = Var [N]...
Discrete Random Variable. The random variable x has the discrete probability distribution shown here: x -2 -1 0 1 2 p(x) 0.1 0.15 0.4 0.3 0.05 Find P(-1<=x<=1) Find P(x<2) Find the expected value (mean) of this discrete random variable. Find the variance of this discrete random variable
Let X be a discrete random variable with pmf p(n) = (n−1)(0.4)2(0.6)n−2, n ≥ 2 and 0 otherwise. Find the mode of X
Let X be a discrete random variable with values in N = {1, 2,...}. Prove that X is geometric with parameter p = P(X = 1) if and only if the memoryless property P(X = n + m | X > n) = P(X = m) holds. To show that the memoryless property implies that X is geometric, you need to prove that the p.m.f. of X has to be P(X = k) = p(1 - p)^(k-1). For this, use...
discrete random variable has probability mass function, P(X = n) = ?1?n. ? 1, forxeven Let Y = −1, for x odd Find the expected value of Y ; (E[y]). probability function mass A discrete random variable has P ( X = n) = (3) for x Y = { for Find the expected value of Y CE(y)] Let even x odd