Suppose that Y is a normally distributed random variable wit

Suppose that Y is a normally distributed random variable with ? = 10 and ? = 2, and X is an independent random variable, also normally distributed with ? = 5 and ? = 5. Find:

P(Y>12 and X>4) (0.088 = 8.8%)

P(Y>12 or X>4) (0.71 = 71%)

P(Y>10 and X<5) (0.25 = 25%)

Solution

P(Y>12 and X>4) = P(Y>12) P(X>4) (as x and y are independent)

= 0.3413(0.5793)

=0.1977

2) P(Y>12 or X>4)

= 0.3413+0.5793-0.1977

= 0.7229 = 72.29%

3) P(Y>10 and X<5)=0.5(0.5)

=0.25 = 25%