Math Problem Solver

1. The chance that a doctor A will diagnose a disease X

correctly is 60%. The chance that a patient will die by

his treatment after correct diagnosis is 40% and the

chance of death by wrong diagnosis is 70%. A patient

of doctor A, who has disease X, died. What is the

probability that his disease was diagnosed correctly?

2. In a tossing of a biased coin head comes three times as often

as tail. If the coin is tossed 3 times, find the probability

distribution of the number of head.

3. The probability function of a random variable X is given by,

1

( ) , 1,2,3,...

2

x

P X x x = = =

Find, (i)P (X is even) (ii) P(X is odd)

(iii) P(X>=4) (iv) P(X is multiple of 3)

4. A continues random variable X has a p.d.f.

2

f x x x ( ) 3 ,0 1 =   .

Find ‘a’ and ‘b’ such that

P X a P X a and P X b ( ) ( ) ( ) 0.05  =   = .

5. A continues random variable X has a p.d.f.

2

,0 1

( ) (3 / 2)( 1) ,1 2

0,

x x

f x x x

otherwise

 

= −   .

Find the cumulative distribution function F(x) of X and use it

to find P(3/2 < X < 5/2).

6. Experience has shown that while walking in a certain park,

the time X (in mins), between seeing two people smoking has

a density function of the form