Question

The number of students using the math lab per day is found in the distribution below. Find the mean, variance, and standard deviation for this probability distribution ? 6 8 10 12 14 ?(?) 0.15 0 0.35 0.1 … Find the (i) Missing probability

Answer 1

X :- 6 8 10 12 14

p(x) :- 0.15 0 0.35 0.1 ....

(1) Missing Probability

let us denote the missing probability by y.

    we know by the axiom of probability that

   

applying it here we get

hence missing probability is given by 0.4.

now probability distribution is

X :- 6 8 10 12 14

p(x) :- 0.15 0 0.35 0.1 0.4

MEAN

fromula of mean is given by

hence

hence mean is given by 11.2.

Variance

formula of variance is given by

we can also write it as

and we already know E(x) = 11.2

now to calculate E(x2)

putting this value in the formula of variance we get

hence var is given by 7.76.

STANDARD DEVIATION

formula of standard devaition is given by

using this

hence standard deviation is given by 2.786.