random probability course Problem 1: [60 points) A discrete random variable has the following probability mass...
A discrete random variable X has the following probability mass function: p(2) DETİ, for x EA; and zero otherwise. 2 T where C is a constant and A is the support of the distribution. Find the value of C if (c) A 12,3,4,5,...) (a) A (0,2,4,6,.. A discrete random variable X has the following probability mass function: p(2) DETİ, for x EA; and zero otherwise. 2 T where C is a constant and A is the support of the distribution....
A discrete random variable, X, has the following probability distribution: P(X) lorem What is the probability that X is not more than 1? (b) What is the probability that X is at least 22|| What is the mean of X? (d) What is the standard deviation of X?
Problem 5 Define X and Y to be two discrete random variables whose joint probability mass function is given as follows: e-127m5n-m P(X = m, Y = n) = m!(n - m)! for m <n, m> 0 and n > 0, while P(X = m, Y = n) = 0 for other values of m, n 1. Calculate the probability that 1 < X <3 and 0 <Y < 2. 2. Calculate the marginal probability mass functions for the random...
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
The discrete random variable X has the following probability mass function: f(x) = kx, for the values of x = 2,4,5 and 6 only. Find the i. value of k. ii. construct the probability distribution of X iii. expected value and standard deviation X
4. (10 points) X are discrete random variables. The following table summarizes the probability mass function of X. X 024 P(x) 0.3 0.35 0.35 Calculate E(X) and V(X).
For Exercises 3-15 to 3-18, verify that the following functions are probability mass functions, and determine the requested probabilities. 3-15. x 2 x)1/8 2/8 2/8 2/8 18 (a) P(Xs 1) (c) P(-1 X (b) P(X-2) (d) P(X--1 1) or X= 2) 3-28. The data from 250 endothermic reactions involving sodium bicarbonate are summarized as follow Final Temperature Conditions 266 K 271 K 274 K Number of Reactions 70 80 100 33. Determine the cumulative distribution function for the random variable...
A discrete random variable X has the following probability distribution: x7778798081 P(x) 0.150.150.200.400.10Compute each of the following quantities. i. P(X = 80) ii. P(x > 80) iii. P(X ≤ 80) iv. The mean, μ of x. v. The variance, σ2 of X. vi. The standard deviation, σ of X.
Problem 4 Let X be the following discrete random variable: P(X-1) = P(X = 0) = P(x-1) Let Y-X2. Show that cov(X, Y) 0, but X and Y are not independent random variable.
Problem 3. Let X be a discrete random variable, with probability distribution P(X X1) = 0.95, P(X X2) = 0.05. Determine x, and X2 such that E(X-0 and σ2(X) = 7.