(i) Four independent flips of a fair coin are made. Let X denote the number of heads obtained. Plot the probability mass function of the random variable X - 2.
(i) Four independent flips of a fair coin are made. Let X denote the number of heads obtained. Plot the probability mass function of the random variable X - 2.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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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![(i) Four independent flips of a fair coin are made. Let X denote the number of heads obtained.
Plot the probability mass function of the random variable X – 2.
(ii) Calculate Var (X), if X represents the outcome when a fair die is rolled. Hint: E[X] = 7/2.
(iii) Suppose that the distribution function of X is given by
0,6 <0
b/4, 0≤b<1
F(b) 1/2+ [(b-1)/4], 1≤ b < 2
11/12, 2<b<3
1, 3≤b
=
(a) Find P{X = i}, i = 1,2,3. (b) Find P{1 < X < 3}.
(iv) On a multiple-choice exam with 3 possible answers for each of the 5 questions, what is the
probability that a student will get 4 or more correct answers just by guessing?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6d6ec3-8d2a-4662-b20e-640089acaa34%2F226a60d4-2a72-4cb3-97c5-0e609d60c829%2Fry60aif_processed.png&w=3840&q=75)
Transcribed Image Text:(i) Four independent flips of a fair coin are made. Let X denote the number of heads obtained.
Plot the probability mass function of the random variable X – 2.
(ii) Calculate Var (X), if X represents the outcome when a fair die is rolled. Hint: E[X] = 7/2.
(iii) Suppose that the distribution function of X is given by
0,6 <0
b/4, 0≤b<1
F(b) 1/2+ [(b-1)/4], 1≤ b < 2
11/12, 2<b<3
1, 3≤b
=
(a) Find P{X = i}, i = 1,2,3. (b) Find P{1 < X < 3}.
(iv) On a multiple-choice exam with 3 possible answers for each of the 5 questions, what is the
probability that a student will get 4 or more correct answers just by guessing?
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