Mathematics

Problem

A discrete random variable

X

takes the values

1,2,3

and

4

with probabilities

2k,\;3k,\;k

and

6k

respectively. Answer the following questions. a. (i) Find the value of

k

so that the above assignments form a probability distribution. b. (ii) Verify that each individual probability obtained in part (i) lies in the permissible range. c. (iii) Using the value of

k

, calculate

P\big(X\ge 3\big)

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