4. Let X be a random variable with distribution P( x =-2) = 1 /2 P(X...
2.1 Let X be a discrete random variable with the following probability distribution Xi 0 2 4 6 7 P(X = xi) 0.15 0.2 0.1 0.25 0.3 a) find P(X = 2 given that X < 5) b) if Y = (2 - X)2 , i. Construct the probability distribution of Y. ii. Find the expected value of Y iii. Find the variance of Y
Let X be a random variable with the following probability distribution: Value x of X P( xx) 0.40 5 0.05 6 0.10 0.35 В 4 7 0.10 Find the expectation E(X) and variance Var (x) of X. (If necessary, consult a list of formulas.) х 5 2
Let X be a random variable with the following probability distribution: Value x of X P(X=x) 0.15 0.10 3 0.05 0.05 0.30 0.35 Find the expectation E (X) and variance Var (X) of X. (If necessary, consult a list of formulas.) E (x) = 0 x 6 ? var(x) -
Let X be a random variable which follows truncated binomial distribution with the following p.m.f. P(X=x) =((n|x)(p^x)(1−p)^(n−x))/(1−(1−p)^n), if x= 1,2,3,···,n. •Find the moment generating function (m.g.f.) and the probability generating function(p.g.f.). •From the m.g.f./p.g.f., and/ or otherwise, obtain the mean and variance. Show all the necessary steps for full credit.
Let x be a random variable with the following probability distribution: Value x of X -2 - 1 0 0 0 1 0 P(X-X) 0.10 .30 .20 .40 Find the expectation E (x ) and variance Var (x) of X. (If necessary, consult a list of formulas.) ( x 5 ? Var (x) - 0
Let X be a random variable with the following probability distribution: Value x of X P=Xx -20 0.25 -10 0.10 0 0.10 10 0.10 20 0.05 30 0.40 Find the expectation EX and variance VarX of X .
Let X be the random variable with the geometric distribution with parameter 0 < p < 1. (1) For any integer n ≥ 0, find P(X > n). (2) Show that for any integers m ≥ 0 and n ≥ 0, P(X > n + m|X > m) = P(X > n) (This is called memoryless property since this conditional probability does not depend on m.)
) 6. Let x be the binomial random variable with n = 10 and p = .9 (2) a. Find P(x = 8) (5) b. Create a cumulative probability table for the distribution. (2) c. Find P( x is less than or equal to 7) (2) d. Find P(x is greater than 7) e. Find the mean, μ. (1) f. Find the standard deviation, σ. (1) g. Find the variance. ...
Let X be a random variable with the following probability distribution: value x of X P (X= x) 40 50 60 70 80 90 0.10 0.15 0.40 0.20 0.05 0.10 Find the expectation E (X) and variance Var(X) of X. (If necessary, consult a list of formulas.) Var(x)-
3. Let X be a random variable from a geometric distribution with parameter p (P(X- k p(1-P)"-, } k-1 k-1, 2, ...). Find Emin{X, 100