Question

3 suppose ‘X’ is normally distributed with mean 20 and variance 8 i.e X-NID

Find

A P(25≤X≤30)

B P(X≥25)

4 Given the following discrete probability destruction.

X 1 5 7 9

F(x) 1/6 2/6 2/6 1/6

Find

A the expected value of x E(X)

The variance of x V(X)

6 the probabilities that Abebe passes microeconomics is 2/3 and the probability that he passed statics 4/9. If the probability of passing both courses is 1/4 ,what is the probability that Abebe will pass at lease one of these courses

Answer 1

3.

A.

$$P(25\le X\le30)=P(Z\le\dfrac{30-20}{\sqrt{8}})$$

$$-P(Z<\dfrac{25-20}{\sqrt{8}})\approx P(Z\le3.5355)$$

$$-P(Z<1.7678)\approx0.0383$$

B.

$$P( X\ge25)=1-P(Z<\dfrac{25-20}{\sqrt{8}})$$

$$\approx1-P(Z<1.7678)\approx0.0385$$

4.

A.

$$E(X)=\dfrac{1}{6}(1)+\dfrac{2}{6}(5)+\dfrac{2}{6}(7)+\dfrac{1}{6}(9)$$

$$=\dfrac{17}{3}$$

B.

$$E(X^2)=\dfrac{1}{6}(1)^2+\dfrac{2}{6}(5)^2+\dfrac{2}{6}(7)^2+\dfrac{1}{6}(9)^2=\dfrac{115}{3}$$

$$Var(X)=E(X^2)-(E(X))^2=\dfrac{115}{3} -(\dfrac{17}{3})^2$$

$$=\dfrac{56}{9}$$

6.

$$P(M\cup S)=P(M)+P(S)-P(M\cap S)$$

$$=\dfrac{2}{3}+\dfrac{4}{9}-\dfrac{1}{4}=\dfrac{31}{36}$$