P&S Assignment

Assignment 2

1 a : for the continous probability function
F(x) = kx2e-x when x >= 0 , find
1. K ; 2. Mean ; 3. Varience.

1 b : a pair of dice are thrown. Let the random ariable x assign to each point (a,B) in S yhe sum of this no’s
1 find the distribution of x
2 the mean of random variables.
1 c : let x be a discrete random variable having the following probability distribution
X -2 -1 0 1 2 3
P(x) .1 k .2 2k .3k 3k
Find : k ; mean ; varience
2 a : pdf f(X) = k(1-x2) for 0 < x < 1 and f(x)=0 otherwise Find : k ; mean; varience 2 b : if x and y are discrete random vriables and k is a constnt. Then prove that 1) E (x+k) = E(X) + k 2) E (x+y) = E(X) + E(Y) 3 a : if x is a continous random variable with distribution F(X) = { 1/6 x+k if 0 <= x <= 3 0 elsewhere Determine : k ; mean ; p(1 <= x <= 2 ) 3 b : the density function of random variable X is f(x) = e-x ; x >= 0
0 otherwise
Find : e(X) ; e(x2) ; varience.
3 c : let x denote the min of 2 no’s that appears when pair of fair dic is tossed. Determine
I discrete probability distribution
Expectation ; varience

4 b : the pdf of a variable xd is
X 0 1 2 3 4 5 6
P(X) k 3k 5k 7k 9k 11k 13 k
Find P( X<4), P(X>=5), p(3 0.3

5 a : if pdf f(x) = kx3 in 0 <= x <= 3
= 0 elsewhere
Find the value of k and find the probability between x=1/2 and x=3/2

5 b : a r.v x has the following probability distrbution
X : 1 2 3 4 5 6 7 8
P(X) : k 2k 3k 4k 5k 6k 7k 8k
Find : k ; p(x <= 2) ; p(2 <= x <= 5)

5 c : if the probabilty density fnctn of x given by
F(x) = x/2 , for 0 < x <= 1
= 1/2 , for 1 < x <= 2
= 3-x /2 , for 2 < x <3
= 0 elsewhere
Find the expected value of f(x) = x2 -5x +3 .

5 d : cal the mean and varinece for the following distribution

X = x -3 -2 -1 0 1 2 3
P(X = x ) .05 .1 .3 0 .3 .15 .1

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