
NOTE : the sum of 1st n natural numbers is n(n+1)/2 which is used in the following problem.
Suppose Y is a discrete random variable with probability mass function p(y) - P(Y -y) -...
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
Let X be a discrete random variable with a probability mass function (pmf) of the following quadratic form: p(x) = Cx(5 – x), for x = 1,2,3,4 and C > 0. (a) Find the value of the constant C. (b) Find P(X ≤ 2).
Find the probability generating function of a discrete random variable with probability mass function given by pX(k) = qk−1p, k = 1,2,..., where p and q are probabilities such that p + q = 1. We shall see later that this is called the geometric distribution function.
Suppose that the probability mass function for a discrete random variable X is given by p(x) = c x, x = 1, 2, ... , 6. Find the value of the cdf F(x) for 3 ≤ x < 4.
X is a negative binomial random variable with parameters. r=1 and P(S)=p p=62/100. Show that the probability mass function for x is well defined. That it satisfies the requirement for any discrete pmf
1. Le us sup pose thai the joint probability mass function of two discrete random variables X and Y be given by to,Y) = (1/18) ( x + 2 y), x=1,2;y=1,2 (C)Find the marginal pmf of X (i) Find the marginal pmf of Y (ii) Are X and γ independent? (iv) Find E (X) ) # Mean μ (v) Find Var (X). wnere Var (X) E (X2)-p? (vi) Find standard deviation of X.
Consider a discrete random variable X with the probability mass function p X ( x ) = x/C , x = 3, 4, 5, 6, 7, zero elsewhere. consider Y = g( X ) = 100/(x^2+1) . b) Find the probability distribution of Y.
Suppose that a random variable X has a discrete distribution with the following probability mass function: Find the value of the constant C.
Let X be a discrete random variable with probability mass function p(k) = 1/5, k = 1, 2, . . . , 5, zero elsewhere. (a) Find the moment generating function of X. (b) Use the moment generating function in (a) to determine the convolution of two identical probability mass functions given above. This is identical to asking the probability mass function of X + Y and where X and Y are independent and each has probability mass function given...
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....