You flip a coin 25 times. Let X; be the Bernoulli random variable indicatingif the i-th coin flip lands on a head.1,X; =| 0, otherwise.if the i-th coin flip lands on a head,Assume that the probability of each coin flip landing on a head is 0.5, and that the 25coin flips are independent.(a) Are X1, X2, ..., X25 i.i.d. (independent and identically distributed)? Briefly explain.(b) Find the expected value ofX1 + X, + .…+X25...25(c) Find the variance of X. (Hint: first compute the variance of X¡.)

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Answered: You flip a coin 25 times. Let X; be the…

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...

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Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of light bulbs that burn out in the next week in a room with 20 bulbs. (b) The weight of a T-bone steak. ... (a) Is the number of light bulbs that burn out in the next week in a room with 20 bulbs discrete or continuous? OA. The random variable is continuous. The possible values are x = 0, 1, 2,..., 20. OB. The random variable is continuous. The possible values are 0≤x≤20. OC. The random variable is discrete. The possible values are x = 0, = 0, 1, 2,..., 20. O D. The random variable is discrete. The possible values are 0≤x≤20. (b) Is the weight of a T-bone steak discrete or continuous? O A. The random variable is discrete. The possible values are w= 1, 2, 3, .... OB. The random variable is continuous. The possible values are w=1, 2, 3, .... OC. The random variable is discrete. The possible values are w> 0. OD. The random variable is continuous.…
A commuter must pass through three traffic lights on her way to work. For each traffic light, the probability that it is green when she arrives is 0.6. The lights are independent. 3 (a) Compute the probability that all three lights are green. (b) The commuter goes to work five days per week. Let X be the number of times out of the five days in a given week that all three lights are green. Assume the days are independent of one another. Determine the distribution of X. (c) Calculate P(X= 3).
A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 5 digits long, and that each digit could be a number between 0 and 6. Assume that the hacker makes random guesses. What is the probability that the hacker guesses the password on her first try? Round to six decimal places. Probability =
??
A student is working on a homework assignment with 5 questions. Each question on the assignment has 3 possible choices, which the student chooses from at random. Assuming that the answers are independent of each other, what is the probability that the student answers all the questions correctly? Report your answer to the 4th decimal place, that is, 0.0025 instead of 0.003.
Pavan
How was the correct answer of 0.0741 attained?

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