Suppose X ~ Pois(3). Find P(X=5)
Select one:
a. 0.2078
b. 0.3001
c. 0.1001
d. 0.1489
Suppose X ~ Pois(3). Find P(X=5) Select one: a. 0.2078 b. 0.3001 c. 0.1001 d. 0.1489
Let X and Y be independent rv’s with pmf Pois(λ1) and Pois(λ2),
respectively.
(a) Find the distribution of Z = X + Y .
(b) Find the distribution of X|X + Y .
(c)If X∼Pois(λ1) and Y|X=x∼Bin(x,p). Find the distribution of
Y.
Let X and Y be independent rv's with pmf Pois(11) and Pois(12), respectively. (a) Find the distribution of Z= X+Y. (b) Find the distribution of X|X +Y. (c) If X ~ Pois(11) and Y|X = x ~ Bin(x,p)....
Let X and Y be independent rv's with pmf Pois(11) and Pois(12), respectively. (a) Find the distribution of Z = X+Y. (b) Find the distribution of X X +Y. (c) If X Pois(11) and Y|X = r ~ Bin(x,p). Find the distribution of Y.
Suppose X~Pois(λ1) and Y~Pois(λ2). Find the conditional mass function for X given X+Y = m
2. (30 pts) Let X and Y be independent rv's with pmf Pois(41) and Pois(12), respectively. (a) Find the distribution of Z = X +Y. (b) Find the distribution of X X +Y. (c) If X ~ Pois(11) and Y|X = x ~ Bin(x,p). Find the distribution of Y.
Suppose X~Pois(A) and Y ~Pois(2A) are independent random variables. Consider a linear estimator of λ, that is, λ = aX + bY. (a) Find an expression for the bias of λ, in terms of a and b, and determine a condition on the values of a and b, such that λ is unbiased. (b) Of all the values of a and b that make the estimator unbiased, find the values of oa and b that minimize the variance of the...
2. (30 pts) Let X and Y be independent rv's with pmf Pois(41) and Pois(12), respectively. (a) Find the distribution of Z = X+Y. (b) Find the distribution of X|X +Y.. (c) If X ~ Pois(11) and Y|X = x ~ Bin(x,p). Find the distribution of Y.
2. (30 pts) Let X and Y be independent rv's with pmf Pois(11) and Pois(2), respectively. (a) Find the distribution of Z = X+Y. (b) Find the distribution of X|X+Y. (c) If X Pois (41) and Y|X = x~ Bin(x, p). Find the distribution of Y.
a. P(X=3)=
b. P(X=3)=
c. P(X=0)=
d. P(X=3)=
Please include Excel formula.
Determine the following probabilities. a. If n 4, N 12, and A 5, find P(X 3). b. If n 4, N 6, and A 3, find P(X 3) c. If n 6, N 11, and A 5, find P(X 0) d. If n 3, N10, and A 3, find P(X 3)
Suppose X is a discrete random variable such that P(X≤1)=0.13P(X≤1)=0.13, P(X≤2)=0.28P(X≤2)=0.28, P(X≤3)=0.43P(X≤3)=0.43, P(X≤4)=0.65P(X≤4)=0.65, P(X≤5)=0.82P(X≤5)=0.82. What is P(2<X<5)P(2<X<5)? Select one: a. 0.22 b. 0.54 c. 0.52 d. 0.69 e. 0.37
Suppose (X,Y) follows a trinomial distribution (5, 1/3, 1/4). a. Find E(X) b. Find E(Y) c. Find Var(X) d. Find Var(Y) e. Find Cov (X,Y) f. Find p (correlation coefficient)