3 Quick Probability questions

1) the secretary of a college has calculated that from the students who took calculus, physics and chemistry last semester:

78% passed calculus

80% passed physics

84% chemistry

60% calculus and physics

65% physics and chemistry

70% calculus and chemistry,

and 55% all three.

Show that these numbers are not consistent, and therefore the secretary has made a mistake

-------------------------------------------------------------------------------------

2) If X is uniformly distributed on {a,b}, find the moment generating function of X

-------------------------------------------------------------------------------

3) that detects missing pulses. The number of errors found in an eight bit byte is a random variable with the following distribution:

F(x)= 0 if x <1

0.7 if 1<= x <4

0.9 if 4<= x <7

1 if x =>7

find the following:

a. P(X<=4)

b) P(X>7)

c) P(X<=2)