) 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)

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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