Question

Three numbers are selected at random (without replacement) from first six positive integers. Let X denote the largest of the three numbers obtained. Find the probability distribution of X.Also, find the mean and variance of the distribution.

Answer 1

X = larger of of three numbers

X = 3, 4, 5, 6

`P(x=3)=6xx1/6xx1/5xx1/4=1/20`

P (x = 4) = `18xx1/6xx1/5xx1/4=3/20`

P (x = 5) = `36xx1/6xx1/5xx1/4=6/20`

P (x = 6) = `60xx1/6xx1/5xx1/4=10/20`

Xi	Pi	PiXi	PiXi2
3	`1/20`	`3/20`	`9/20`
4	`3/20`	`12/20`	`48/20`
5	`6/20`	`30/20`	1 `50/20`
6	`10/20`	`60/20`	`360/20`

`"Mean"=sumP_iX_i=(105/20)=5.25`

`sumP_iX_i^2=567/20`

Var(X)= `sumP_iX_i^2-(sumP_iX_i)^2`

`=567/20-(105/20)^2=0.787`