Suppose X₁, X₂~ iid N(0,1) Calculate the probability P(X² + X² < 4.605) Use the fact that square of a standard normal is a chi square with 1 degree of freedom. And sum of independent chi squares is a chi square with degrees of freedom added.

Suppose X₁, X₂~ iid N(0,1) Calculate the probability P(X² + X² < 4.605) Use the fact that square of a standard normal is a chi square with 1 degree of freedom. And sum of independent chi squares is a chi square with degrees of freedom added.

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

The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.
The amount of time it takes Susan to wait for the bus is continuous and uniformly distributed between 4 minutes and 18minutes. What is the probability that it takes Susan less than 5 minutes given that it takes less than 11 minutes for her to wait for the bus
Let X be a random variable with a uniform distribution over the interval [-2 , 4]. Determine the mean of X. The answer should be a number rounded to five decimal places
Suppose that the time. in days, required to repair a heat pump is a random variable X having a gamma distribution with parameters k = 8 and A = 2. What is the probability that on the next service call (a) at most 3 day will be required to repair the heat pump? (b) at least 2 days will be required to repair the heat pump? %3D %3D
Use normal approximation to estimate the probability of getting less than 46 girls in 100 births. Assume that boys and girls are equally likely.
Suppose that a medical test has a 85% chance of detecting a disease if the person has it (P(PT|D)=0.85) and a 90% chance of correctly indicating that the disease is absent if the person really does not have the disease (P(NT|Dc=0.90). Suppose that 95% of the population does not have the disease P(Dc)=0.95 What is the probability that a randomly chosen person will test negative P(NT)?
I have a probability distribution consisting of (x, p(x)): (-3, 0.1), (-2, 0.2), (-1, 0.3), (0, 0.05). The probabilities obviously do not sum to 1. How do I find <x> (average), <x2> (the second moment), <sigmax2> (the variance)?