Mathematics

Problem

A discrete random variable

W

assumes the values

1,2,3,

and

4

with probabilities

k,\;2k,\;m,

and

m+0.10

respectively. It is also known that the probability of obtaining an even value is

0.55

. Answer the following questions. a. (i) Using the given information, form two independent equations in

k

and

m

. b. (ii) Solve the equations and determine the values of

k

and

m

. c. (iii) Verify that each probability obtained in part (ii) lies between

0

and

1

, thereby confirming that the assignments constitute a valid probability distribution. d. (iv) Find

P\big(W\le 3\big)

using the values of

k

and

m