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.

College Algebra (MindTap Course List)
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Author:R. David Gustafson, Jeff Hughes
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Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...
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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).
Transcribed Image Text: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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