Suppose the random variable has possible values {1, 2, 3, 4, 5, 6} and that the probability mass function is given by p(x) = (cx for x = 1, 2, 3, 4, 5, 6 0 otherwise) (a) Find the value of c that makes p(x) a valid PMF. (b) Compute E[X]. (c) Compute E[X^2]. (d) Compute the standard deviation of X, SD(X). (e) What is the probability that X is within 2 standard deviations of its mean; that is, calculate P(E[X] − SD(X) < X < E[X] + SD(X)).

Suppose the random variable has possible values {1, 2, 3, 4, 5, 6} and that the probability mass function is given by p(x) = (cx for x = 1, 2, 3, 4, 5, 6 0 otherwise) (a) Find the value of c that makes p(x) a valid PMF. (b) Compute E[X]. (c) Compute E[X^2]. (d) Compute the standard deviation of X, SD(X). (e) What is the probability that X is within 2 standard deviations of its mean; that is, calculate P(E[X] − SD(X) < X < E[X] + SD(X)).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: (6) Let X be a Poisson random variable with parameter 0, then E(X²) = 1. От OF

A: Poisson distribution is the type of discrete probability distribution. It explain the number of…

Q: A random variable W has range RW = {1, 2, 3, . . . } and the probability mass function given by…

A: The provided information is as follows:The is a random variable having a range .The probability…

Q: Suppose the number of people in a gym each morning has a Poisson distribution, but with the rate…

A: Step 1 Part (a): Create Prior Distribution for λ 1. Lambda Vector: Generate a vector of λ values…

Q: 7. If X is a random variable with fx Let Y = 3√In X. (a) Fx(x) ) = 1, 1<x<e (b) Fy(y) (c) fy(y)

Q: Suppose that X1, X2, X3 are independent with the common probability mass function: P{Xi = 0} = 0.2,…

A: Let X1,X2,and X3 be independent random variables with the common probability mass function (PMF)…

Q: Q4) Assume that a variable x comes from a probability distribution of the form P(x|w) exp(Σwkf(x) 1…

Q: Suppose the random variable X~ Beta(a, 3), namely its PDF fx(x) = I(a + B) r(a)r(3)* r^-1(1−z)ß-1, 0…

A: Solution

Q: A random variable W has range RW = {1, 2, 3, . . . } and the probability mass function given by…

A: P(W=k)=1k2kln(2);k=1,2,3...,Objective:Find the expected value of W:Concept Used : Geometric series:…

Q: Let X1,, X, denote a random sample of size n from the population with probability density function…

Q: Let X be a discrete random variable with possible values {0,1,2,...} and the following probability…

A: Given: (a) The provided function can be said probability mass function, if its probability is 1.…

Q: ) Write the joint probability density function. p) Express F(z) = P(¥ <z) using integrals and…

A: Let X and Y be continuous independent random variable have exponential distribution with mean θ

Q: (b) Assume that Y₁, Y₂, ..., Yn are independent normal random variables with mean μ = B₁ + B₁x₂ and…

Q: Let p(x) = cx^2 for the integers 1, 2, and 3 and 0 otherwise. What value must c be in order for p(x)…

A: Solution: From the given information, the probability mass function of X is

Q: 0, x)

A: a) The required value is calculated as follows: fx=ddxFx =ddxx24 =2x4 =x2…

Q: a. The probability density function for X is f(x) = e¬× , x > 0, zero, e.w. Find the probability…

Q: If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?

A: is a continuous random variable following a uniform distribution, that is .

Q: Suppose that the continuous random variable X has CDF Fx(X) = {(x-2)/x , x>2 and 0, x=<2} a.…

Question

Suppose the random variable has possible values {1, 2, 3, 4, 5, 6} and that the probability mass function is given by
p(x) = (cx for x = 1, 2, 3, 4, 5, 6
0 otherwise)
(a) Find the value of c that makes p(x) a valid PMF.
(b) Compute E[X].
(c) Compute E[X^2].
(d) Compute the standard deviation of X, SD(X).
(e) What is the probability that X is within 2 standard deviations of its mean; that is, calculate
P(E[X] − SD(X) < X < E[X] + SD(X)).

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: State the problem

VIEW

Step 2: Find the constant

VIEW

Step 3: Calculate the expectation

VIEW

Step 4: Calculate the second order raw moment

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let X (X1, X2,..., Xn) be a sample of i.i.d. Poisson(0) random variables with probability mass %3D function e-gz f(x, 8) = Po(X = x) = æ! x € {0,1, 2, .}, 0 > 0. The statistic T(X) = Ei-1Xi is complete and sufficient for 0. i3D1 Derive the UMVUE of h(0) = e_kU where k = 1, 2, ... , n is a known integer. Hint: Use the interpretation that P(X1= 0) = e-º and therefore we have that P(X1 = 0,.., Xk = 0) = P(X1 = 0)* = e¬k® and also note that n T(X) = X; ~ Poisson(n0). i=1 (-) Pumvue 1 - 1 ( t Îumvue Îumvue = (-)' humvue (-)" Îrumvue
Two discrete random variables X and Y have joint probability mass function (pmf) (a) (b) (c) ƒ(x) = { 5 0 Calculate the value of k. Show that f(x|y) Show that f(y x) = k n(n+1) = 1 n 1 8 x = 1,2,..., n; y=1,2,...,x. otherwise
Let (Ω, Pr) be a probability space, and let X and Y be two independent random variables that are positive and have non-zero variance. (a) Prove that X^2 and Y are independent. Note that by symmetry, it will also follow that Y^2 and X are independent. (b) Use the result from part (a) to show that the random variables W = X + Y and Z = XY are positively correlated (i.e. Cov(W, Z) > 0).
Let X1,...,X, be independent random variables with pdfs -{* 0 -i(0 – 1) 0. Find a two-dimensional sufficient statistic for 0.
1 (20') The discrete type random variable X has PMF Px(1)= { c(5- ) for a= 1,2, 3, 4 0, otherwise. (a) Determine the value of c. (b) Find E[X] and Var[X]. (c) Find the probability P[X > 2].
Let X and Y be two random variables with joint probability mass function: p(x,y) = xy(1+y) for X=1,2,3 and Y=1,2 p(x,y) = 0, Otherwise. Please enter the answer to 2 decimal places. • What is the variance of (4-5X)?
Exercise 10. For an exponential random variable X (Definition 10), show that E[X] = }. More generally, for a function o : R R, E(¢(X)] = | (u) dF(u) (5.4)
Let X be a Gaussian RV on with expected value (mean) E[X] = 1, Var[X] = 1. Let Y = -3(X-1). Compute the expected value of Y. QUESTION 7 Let X be a Gaussian RV on with expected value (mean) E[X] = 1, Var[X] = 1. Let Y = -3(X-1). Compute the variance of Y.
Suppose that Z1, Z2, . . . , Zn are statistically independent random variables. Define Y as the sum of squares of these random variables