statistics 2 - probability distribution GRAPH

This is from a past paper of S2.

In a town, 30% of residents listen to the local radio station. Four residents are chosen at random

(a) State the distribution of the random variable X (the number of these four residents that listen to the local radio station).

(b) On Graph paper, draw the probability distribution of X

(c) Write down the most likely number of these four residents that listen to the local radio

(d) Find E(x) and Var (x)

Any help with parts b and onwards would help. Part (a) is X~B(4, 0.3)

Cheers!

Reply 1

m:)ckel

b)
P(X=0) = 0.7^4
P(X=1) = 4(0.3)(0.7)^3
P(X=2) = 6(0.3)^2(0.7)^2
P(X=3) = 4(0.3)^3(0.7)
P(X=4) = (0.3)^4

Now it's just a matter of calculating these values and plotting a bar chart, with P(X=x) as your y-axis and X= 1 to 4 on your x-axis

c) Whichever figure in a) is the highest

d)
E(X) = (Sum of) x.P(X=x) = (1)[4(0.3)(0.7)^3] + (2)[6(0.3)^2(0.7)^2] + (3)[4(0.3)^3(0.7)] + (4)[(0.3)^4]

Var(X) = E(X^2) - [E(X)]^2 = (1²)[4(0.3)(0.7)^3] + (2²)[6(0.3)^2(0.7)^2] + (3²)[4(0.3)^3(0.7)] + (4²)[(0.3)^4] - [E(X)]^2

(where E(X) is calculated above)

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