A discrete random variable, X, has probability distribution as given inthe table below.a)p(X = x)3.0.150.25k0.45120.2i.E(X) = 8.45 Find the value of k.b)A and B are two events such that p(A) = 0.4 and p(B) = 0.75.Events A and B are independent.i.Find p(A n B) and p(A U B).ii.Draw a Venn diagram to show these probabilities.iii. Hence work out p(A' n B), p(AU B') and p(A' | B).

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Answered: A discrete random variable, X, has…

A discrete random variable, X, has probability distribution as given in the table below. 3 k 12 p(X = x) 0.1 0.25 0.45 0.2 E(X) = 8.45 Find the value of k.

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Question

A discrete random variable, X, has probability distribution as given in
the table below.
a)
p(X = x)
3.
0.1
5
0.25
k
0.45
12
0.2
i.
E(X) = 8.45 Find the value of k.
b)
A and B are two events such that p(A) = 0.4 and p(B) = 0.75.
Events A and B are independent.
i.
Find p(A n B) and p(A U B).
ii.
Draw a Venn diagram to show these probabilities.
iii. Hence work out p(A' n B), p(AU B') and p(A' | B).

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