Find the value of c for which p(x) defined below is a probability mass function: (a)...
Find the value of c for which p(x) defined below is a probability mass function: (a) p(x) = cx?, x= 1,2,3. (b) p(x) = (-X, x= 1,2,3,...
2. The probability mass function below is defined for x 0, 1,2,3,.. fr 5 5 -56 What is the probability for each of the following expressions? a) P(X 2) b) P(XE 2) c) P(X> 2) d) P(X2 1)
Find the value of C for which the following function
will be a probability function.
(c) f(x)= cx" (1 – x)°, 0<x< 1
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).
Answer number 3, please.
2. The probability mass function below is defined forx - 0, 1,2,3,... 32 f(x)- What is the probability for each of the following expressions? a) P(X 2) b) P(X S2) c) P(X>2) d) P(X2 1) Determine values of the cumulative distribution function for the random variable in the previous problem 3.
5. Random variables X and Y have joint probability mass function otherwise (a) Find the value of the constant c. (b) Find and sketch the marginal probability mass function Py (u). (c) Find and sketch the marginal probability mass function Px (rk). (d) Find P(Y <X). (e) Find P(Y X) (g) Are X and Y independent? 2 内?
(a) Consider a Poisson distribution with probability mass function: еxp(- в)в+ P(X = k) =- k! which is defined for non-negative values of k. (Note that a numerical value of B is not provided). Find P(X <0). (i) (4 marks) Find P(X > 0). (ii) (4 marks) Find P(5 < X s7). (ii) (4 marks) 2.
2. The random variable, X has the following probability mass function (i) Find the value of the constant c. HINT: It will help to use the identity = (i) Find the cumulative distribution function of X and sketch both the probability mass function and the cumulative distribution function NOTE: Think carefully about the values of r for which you need to define the distribution function. (ii) Calculate P(X 2 50) and PX 2 50 x2 40
Consider the geometric random variable X with probability mass function P(X =x)=(1 p)x 1p, x=1,2,3,.... For t <- l o g ( 1 - p ) , c o m p u t e E [ e t X ] .
Let the probability mass function of X be given as 5. | | P(X-x) a) Find the pmf of Y2 b) Find the pmf ofY X2 0.3 0.60
Let the probability mass function of X be given as 5. | | P(X-x) a) Find the pmf of Y2 b) Find the pmf ofY X2 0.3 0.60