PSQT - Cycle Test 2

Cycle Test 2
PSQT

PART - A
1. Define Poisson Distribution
2. If X is a Binomial Variable with expected value 6 and variance 2.4, find P(X=5)
3. If X and Y are independent Poission variate s.t P(X=1)=P(X=2) and P(Y=2)=P(Y=3). Find Variance of X-2Y
4. If X is a Geometeric variate taking values 1,2,...., find P(X is odd)
5. Derieve the mean and variance of Negative Binomail Distribution
6. Tabulate teh Expectations for both Discrete nad Continuous Random Variable
7. Define CoVariance. If X and Y are independent RVs, PT E(XY)=E(X).E(Y)
8. What is Gamma Distrinution? Generate its Formula.
9. Show that for a uniform distrbution in (a,b) then f(x)={1/b-a,a<x<b}
10. Find the mean and variance fo the continuous random variable 'X', if it has the density function f(x={2(x-1),1<x<2}

PART - B
11. Determine the Moment generating function of Binomial and Poisson distribution in discrete distribution
12. A random variable Y is defined as Cos(PI x), where X is a uniform PDF over (-1/2,1/2). Find mean and SD
13. Generate the MGF, Mean and Variance of Exponential Distribution Distribution. Give one example for each.
14. Give the PDF of a cantinuous Random Variable 'X' as follows f(x)=6x(1-x), 0<x<1. Find the CDF for 'X'

Tags : cycle test, cycle test 1, 2012, probability statistics and queuing theory, sem 4