Consider a random variable X with PMF Px(X) ={ cx x = 1,2,...,5 I found the...

Question

Question

Consider a random variable X with PMF Px(X) ={ cx x = 1,2,...,5

I found the value of c to be 1/15

1. find the complete expression for the CDF of X. 2. Find E[X], the expected value of X.

Answer 1

Answer #1

The probability mass function of X is

1. The cumulative distribution function(CDF) of X is

2. The expected value of X is

Answer 2

Similar Homework Help Questions

Consider independent random variables X\,X,,.. with PMF 0.3, if x =0, Px (x){0.2, if x =...

Consider independent random variables X\,X,,.. with PMF 0.3, if x =0, Px (x){0.2, if x = 1, 0.5, if x = 2 (a) Find the MGF (s) and E[X7), (b) Let WnX+X2+ .+ X. Find ør (s) and find P[W3 = 5] using r(s) (c) Find P[10 < W10 < 12] by using n 1,2 by using øx(s). appropriate approximation an
a) In each of the following pmfs, find the value of C. i) p(x) Cx, x...

a) In each of the following pmfs, find the value of C. i) p(x) Cx, x 1, 2, 3, 4, 5 ii) p(x) C/x, 2,4,8, 16 b) Assume that the pmf of a discrete random variable X is given by px (x) = 20x-, x = 1, 2, 3, Calculate the following probabilities: i) P(X <3) ii) E[X]
Supposing that X is a given random variable with its pmf given. CX for x =...

Supposing that X is a given random variable with its pmf given. CX for x = 1,2,3,4 0. W. (a (6) f(x) = 0 Determine the value of the constant c. Let W = -4X + 20. Find E(W).

5. Let X be a discrete random variable with the following PMF: for x = 0...

5. Let X be a discrete random variable with the following PMF: for x = 0 Px(x)- for 1 for x = 2 0 otherwise a) Find Rx, the range of the random variable X. b) Find P(X21.5). c) Find P(0<X<2). d) Find P(X-0IX<2)
Suppose that X is a continuous random variable with density pX(x) = ( Cx(1 − x)...

Suppose that X is a continuous random variable with density pX(x) = ( Cx(1 − x) if x ∈ [0, 1] 0 if x < 0 or x > 1. (a) Find C so that pX is a probability density function. (b) Find the cumulative distribution of X. (c) Calculate the probability that X ∈ (0.1, 0.9). (d) Calculate the mean and the variance of X. 9.) Suppose that X is a continuous random variable with density C(1x) if E...
Px(x) = The marginal pmf of each of X, Y variables is given below: 1 ;...

Px(x) = The marginal pmf of each of X, Y variables is given below: 1 ; x = -1,3 4 y + 1 2 PY) = ; y = 1,2 - ; x = 1 5 4 0; Otherwise 0; Otherwise (a) If X, Y are independent random variables, then obtain and report the complete joint pmf of X, Y. Provide your answer in a tabular or functional form. (b) Compute the probability that sum of X and Y is...

Let ? be a positive integer random variable with PMF of the form ??(?)=12⋅?⋅2−?,?=1,2,…. Once we...

Let ? be a positive integer random variable with PMF of the form ??(?)=12⋅?⋅2−?,?=1,2,…. Once we see the numerical value of ?, we then draw a random variable ? whose (conditional) PMF is uniform on the set {1,2,…,2?}. 1.1 Write down an expression for the joint PMF ??,?(?,?). For ?=1,2,… and ?=1,2,…,2?: ??,?(?,?)=? 1.2 Find the marginal PMF ??(?) as a function of ?. For simplicity, provide the answer only for the case when ? is an even number. (The...
3 (17') The random variable X obeys the distribution Binomial(n,p) with n=3, p=0.4. (a) Write Px(x),...

3 (17') The random variable X obeys the distribution Binomial(n,p) with n=3, p=0.4. (a) Write Px(x), the PMF of X. Be sure to write the value of Px(x) for all x from - to too. (b) Sketch the graph of the PMF Px [2] (c) Find E[X], the expected value of X. (d) Find Var[X], the variance of X.
0.25 x-1 0.15 x2 6. Let X be a discrete random variable with PMF: Px(x) 0.2...

0.25 x-1 0.15 x2 6. Let X be a discrete random variable with PMF: Px(x) 0.2 x-3 0.1 x 4 0.3 x-5 0 otherwise a. (10 points) Find E[X] b. (5 points) Find Var(X)

The random variable X has CDF 0 <-1, Ex(x) = 0.2 -1 < 0, 0.7 0...

The random variable X has CDF 0 <-1, Ex(x) = 0.2 -1 < 0, 0.7 0 x<1, 1 21. (a) Draw a graph of the CDF (b) Write Px(), the PMF of X. Be sure to write the value of Px(a) for all r from-oo to oo. Given the random variable X in problem ii), let V g X)X. (a) Find P(v). (b) Find Fy(v). (c) Find EIV]