Let f(x) = b(x+1), x = 0, 1, 2, 3 be the probability mass function (pmf)...

Let f(x) = b(x+1), x = 0, 1, 2, 3 be the probability mass function (pmf) of a random variable X, where b is constant.

A. Find the value of b

B. Find the mean μ

C. Find the variance σ^2

Expert Solution

A. The value of b=0.1

B. The value of mean μ= 2

C.The value of variance σ^2 = 1

The detailed answer is given in the attached file. Hope this helps.

orchestra answered 2 years ago

Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2,...

Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2, f(1, 0) = 3, f(1, 1) = 5, f(2, 0) = 5, f(2, 1) = 10. Determine the Lagrange interpolation F(x, y) that interpolates the above data. Use Lagrangian bi-variate interpolation to solve this and also show the working steps.

Let be the following probability density function f (x) = (1/3)[ e ^ {- x /...

Let be the following probability density function f (x) = (1/3)[ e ^ {- x / 3}] for 0 <x <1 and f (x) = 0 in any other case a) Determine the cumulative probability distribution F (X) b) Determine the probability for P (0 <X <0.5)

a. For the following probability density function: f(X)= 3/4 (2X-X^2 ) 0 ≤ X ≤ 2 &nbsp

a. For the following probability density function: f(X)= 3/4 (2X-X^2 ) 0 ≤ X ≤ 2 = 0 otherwise find its expectation and variance. b. The two regression lines are 2X - 3Y + 6 = 0 and 4Y – 5X- 8 =0 , compute mean of X and mean of Y. Find correlation coefficient r , estimate y for x =3 and x for y = 3.

Let X1 and X2 be a random sample from a population having probability mass function f(x=0)...

Let X1 and X2 be a random sample from a population having probability mass function f(x=0) = 1/3 and f(x=1) = 2/3; the support is x=0,1. a) Find the probability mass function of the sample mean. Note that this is also called the sampling distribution of the mean. b) Find the probability mass function of the sample median. Note that this is also called the sampling distribution of the median. c) Find the probability mass function of the sample geometric...

Let X has the probability density function (pdf) f(x)={C1, if 0 < x ≤ 1, C2x,...

Let X has the probability density function (pdf) f(x)={C1, if 0 < x ≤ 1, C2x, if1<x≤4, 0, otherwise. Assume that the mean E(X) = 2.57. (a) Find the normalizing constants C1 and C2. (b) Find the cdf of X, FX. (c) Find the variance Var(X) and the 0.28 quantile q0.28 of X. (d)LetY =kX. Find all constants k such that Pr(1<Y <9)=0.035. Hint: express the event {1 < Y < 9} in terms of the random variable X and...

Consider a discrete random variable with the following probability mass function x 0 1 2 3...

Consider a discrete random variable with the following probability mass function x 0 1 2 3 4 5 p(x) 0.1 0.1 0.2 0.3 0.2 0.1 Generate a random sample of size n =10000 from this distribution. Construct a bar diagram of the observed frequencies versus the expected frequencies.(using R)

Let f(x,y)= (3/2)(x^2+y^2 ) in 0≤x≤1, 0≤y≤1. (a) Find V(X) (b) Find V(Y)

A discrete random variable named X has the following pmf (probability mass function): X P(x) 1...

A discrete random variable named X has the following pmf (probability mass function): X P(x) 1 0.6 3 0.2 7 0.1 11 0.1 17a) Find P(X>6) 17b) What is the probability two independent observations of X will both equal 1? 17c) Find the population mean also known as E(X)= the expected value of 17d) Find the population variance of X with both the “regular” formula and “convenient” formula Make a table and show your work. You should get the same...

Function f (x) = a x + b for IxI < 2 = 0 for x others...

Function f (x) = a x + b for IxI < 2 = 0 for x others Determinate Fourier series from n= 0 until n= 2

Define the joint pmf of (X, Y) by f(0, 10) = f(0, 20) = 1 /...

Define the joint pmf of (X, Y) by f(0, 10) = f(0, 20) = 1 / 24, f(1, 10) = f(1, 30) = 1 / 24, f(1, 20) = 6 / 24, f(2, 30) = 14 / 24 Find the value of the following. Give your answer to three decimal places. a) E(Y | X = 0) = b) E(Y | X = 1) = c) E(Y | X = 2) = d) E(Y) =

Question