Exercise 6 Suppose that X and Y are independent Poisson random variables with parameters 1and 2, respectively. Decide whether the probabilities are calculated the right way.a) P(X = 1 and Y = 2) = 0.0996 (rounded);b) P(X±Y ≥ 1) = 0.9023 (rounded);2c) P(X = 1|X±Y = 1) = 0.4444 (rounded);2

The Poisson Probability Distribution Function is given by: P(X=x) = e-λλxx! ; x= 0,1,2,3,4,5,...…

Answered: Exercise 6 Suppose that X and Y are…

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

Assume that X₁, X2,..., Xn are independent and identically distributed random variables with expectation and finite variance o2. What is the approximate distribution of Sn = X₁ + X₂ + + Xn? (State all parameters of the distribution.)
Consider a Poisson random variable X with μ = 7.5. Use the Poisson formula to calculate the following probabilities. (Round your answers to six decimal places.) (a) P(X = 0) (b) P(X= 1) (c) P(X = 2) (d) P(X ≤ 2)
Please be specific.
Let Y be a binomial random variable with n = 10 and p = 0.3. (a) P(3 < Y < 5) = P(3 ≤ Y < 5) = (b) P(3 < Y ≤ 5) = P(3 ≤ Y ≤ 5) =
Assume X and Y are independent random variables with X ~ Binomial(n =100, p = 0.2) and Y ~ Pascal(m =16, p = 2/3) . Find the indicated expected value and variance. a. E(3X + 2Y +1) b. Var(3X + 2Y +1)
Let x be a poisson random variable with mean = 6.5. Find the probabilities of x using the poisson formula. A) P(x=0) B) P(x=1) C) P(x=2) D) P(x
Consider the random sample X1, ... , X4 from a Uniform distribution (0,1). Calculate the expectation of the random variable: Y1 = min( X1, ... , X4)
Let X be a normal random variable with = 9 and o 1.85 and Y be a normal random variable with u = 3 and o 0.45. Assume X and Y are independent. Find the following probabilities: (a) P(X 8, Y 3.75) (d) P(X < 12, 2.1 ≤Y ≤ 3.8)
Let Y1, Y2, Y3 denote independent exponential random variables with respective rates A; for i e {1,2, 3}. Answer the following questions; (a) Compute E[Y1 +Y2 +Y3]Y1 > 1, Y2 > 2, Y3 > 3]. Your answer should be an expression using A;'s. (b) Compute the probability that Yı is the smallest among three random variables. Hint: P(X < Y) = S" Px,y (x, y)dædy where Px,Y (x, y) is the joint density function.
Let X be a binomial random variable with mean u = 2.2 and variance o2 = 1.76, find a) Write the probability distribution function. b) P(x<2) c) If Y = 0.5 X - 0.4, find the mean and variance of the new random variable Y.
Suppose that the number of customers entering a bank in one hour is a Poisson random variable and suppose that P(X=0)=0.02. Find the mean and variance of the variable. X: Number of customers entering a bank in one hour E(X)= Answer (Give the exact answer) V(X)= Answer (Give the exact answer) What is the probability that 5 customers will enter in two hours? Answer: Note: Answer with at least 4 decimal places
X has been defined as the Poisson random variable. Thus, P (X = 1) = 0.149 and P (X = 2) = 0.224 are given. Find out what the probability P (X = 0) is.

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

Exercise 6 Suppose that X and Y are independent Poisson random variables with parameters 1 and 2, respectively. Decide whether the probabilities are calculated the right way. a) P(X = 1 and Y = 2) = 0.0996 (rounded); b) P(X±Y ≥ 1) = 0.9023 (rounded); c) P(X = 1|X±Y = 1) = 0.4444 (rounded);