Suppose that X is a discrete random variable,and suppose that the probability massfunction of X is given as follows: p(0) = 0.4,p(10) = 0.3, p(20) = 0.2 and p(30) = 0.1.a) The expected value of Xisb) The variance of Xisc) The probability that X is at most 20 isd) The probability that Xis at least 20 is

Given that Probability distribution table. X 0 10 20 30 P(x) 0.4 0.3 0.2 0.1 NOTE:-…

Answered: Suppose that X is a discrete random…

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

Similar questions

If X is a uniformly distributed random varibale with a=8 and b=13, then Calculate the mean and variance of X? Round to three decimal places
Suppose you have a sample of 9 observations Y1,...,Y, from a normal population with mean 2 and variance 4. Let Y and S denote the sample mean and sample variance, respectively. What is the distribution of E ( (a) (b) 653 (c) Suppose X1,X2, X3, X4, X5 are independent random variables from a normal population with mean 0 and variance 4. Define S3 = E(X, - X). What is the distribution of 253 + S3?
3) Suppose X is a discrete variable that has the following pr function (pdf) f (X) 1. 0.40 0.20 3 0.15 4. 0.25 a) Calculate the cumulative distribution function (the b) Find the expected value, showing your work: E(X) c) Find the variance, showing your work: Var (X)
9. Zero-mean Gaussian random variables x and y have variance oz= 3 and o= 4 respectively and a y -1 correlation coefficient p = ing Write an expression for the joint density function.
Consider the following simple linear regression. iid Y = Po + B₁X + e, e~ N(0,02), i=1,..., n.
Let Y, represent the ith normal population with unknown mean #, and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size n,, from the ith population with sample mean Y, and sample variance S² = (₁-P) ². (d) Define V₁, a function of S1, that has a chi-square distribution. (e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument. (f) Find a (1-a) x 100% confidence interval for of
If the random variable X as a mean of u and a variance of o2 what is the P((X-u)² < 20): O less that equal to 1/4 O greater than or equal to 3/4 cannot tell O equal to 5/4
Consider a random variable V modeling the version of the software that people have installed on their computers, where the possible versions are {1, 2, 3, 4}. People are equally likely to have versions 1 and 2 and also equally likely to have versions 3 and 4. People are also x times more likely to have version 3 than version 2. (a) What is the (probability mass function) PMF of V as a function of x (b) What is the expected version of the software. Hint: the expected value of V as a function of x (c) What is the minimum value of x to ensure that the mean version is at least version 3?
Suppose that X is a discrete random variable with the probability mass function given by: where i = 1,2,3 .8 36 a) Plot p(x) b) Compute and plot F(x) c) Compute (i) P (2.9999
Identify the distributions of the random variables with the following moment- generating functions and derive the mean and the variance: a) My(t) = (1 – 4t)-2 b) My(t) = e-5t+6t² %3D
Assume that a random variable Y has a mean of zero and standard deviation of one. Calculate the expected value of X1 and X2 if they are defined as below. X1 = Sigma+ Mu X2 = Sigma(Y+Mu)
ans Theorem 9.3. Let X and Y be independent random variables with finite variances, and a, b ER. Then Var(aX) = a²Var (X), Var (X+Y) = VarX + Var Y, Var (ax + bY) = a²VarX + b²Var Y. sercise Prove the theorem. Remark 9.2. Independence is sufficient for the variance of the sum to be equal to the sum of the variances, but not necessary. Remark 9.3. Linearity should not hold, since variance is a quadratic quantity. Remark 9.4. Note, in particular, that Var (-X) = Var(X). This is as expected, since switching the sign should not alter the spread of the distribution.

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

Suppose that X is a discrete random variable, and suppose that the probability mass function of X is given as follows: p(0) = 0.4, p(10) = 0.3, p(20) = 0.2 and p(30) = 0.1. a) The expected value of Xis b) The variance of Xis