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) Suppose that the random variable, X, is a number on the biased die and the p.d.f. of X is as shown below; X 1 2 3 4 5 6 P(X=x) 1/6 1/6 1/5 k 1/5 1/6 Find; (i) the value of k. (ii) E(X) (iii) E(X2) (iv) Var(X) (v) P(1 X <5) (b) If events A and B are such that they are independent, and P(A) = 0.3 with P(B) = 0.5; i. Find P(A n B) and P(AUB) ii. Are A and B mutually exclusive? Explain. (c) In how many ways can the letters of the word STATISTICS be arranged? (c) State three (3) characteristic properties of a Normal Distribution curve.

) Suppose that the random variable, X, is a number on the biased die and the p.d.f. of X is as shown below; X 1 2 3 4 5 6 P(X=x) 1/6 1/6 1/5 k 1/5 1/6 Find; (i) the value of k. (ii) E(X) (iii) E(X2) (iv) Var(X) (v) P(1 X <5) (b) If events A and B are such that they are independent, and P(A) = 0.3 with P(B) = 0.5; i. Find P(A n B) and P(AUB) ii. Are A and B mutually exclusive? Explain. (c) In how many ways can the letters of the word STATISTICS be arranged? (c) State three (3) characteristic properties of a Normal Distribution curve.

A First Course in Probability (10th Edition)
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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Question

a) Suppose that the random variable, X, is a number on the biased die and the p.d.f. of
X is as shown below;

X

1

2

3

4

5

6

P(X=x)

1/6

1/6

1/5

k

1/5

1/6


Find;
(i) the value of k.
(ii) E(X)
(iii) E(X2)
(iv) Var(X)
(v) P(1 X <5)
(b) If events A and B are such that they are independent, and P(A) = 0.3 with P(B) = 0.5;
i. Find P(A n B) and P(AUB) 
ii. Are A and B mutually exclusive? Explain. 
(c) In how many ways can the letters of the word STATISTICS be arranged? 
(c) State three (3) characteristic properties of a Normal Distribution curve. 

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