AREG NO
MODEL EXAM DEC-2013DEPARTMENT OF CSE (M.E.)SUB CODE:
MA7155MAX.MARKS :100SUB NAME: APPLIED PROBABILITY &
STATISTICSDURATION: 3 HrsSEMESTER/ YEAR: I/IDATE:
Answer ALL QuestionsPART-A (10x2=20)1. If RV X has the mfg.
Obtain the S.D. of X.2. If X is a continuous random variable with.
Find the value of k.3. If f(x,y) = , for 0 x < 2 and 0 < y
< 2 is the jdf of X and Y. Find the marginal distribution of
X.
Show that 4. The two equations of the variables X and Y are x =
19.13 0.87y and y = 11.64 0.50x. Find the mean of X and Y.5. Find
the MLE of for a normal population N(,2).6. What are the expected
frequencies of 2 2 contingency table given below? ab
cd
7. The heights of college students in Chennai are normally
distributed with SD 6 cm and sample of 100 students had their mean
height 158 cm .test the hypothesis that the mean height of college
students in Chennai is 160 cm at 1% level of significance.8. Derive
expression for the mean and variance for the linear combination X1
2X2 in terms of the means and covariance of the matrix of the
random variable X1& X2.
Let X be distributed as N3(,), where = [1, 1, 2] and . Verify
random variables X1& X2 are
independent.me2013regulation.wordpress.com
PART B (5x16 = 80)11.(a) A discrete random variable X has the
probability function given belowX01234567
P(X)0a2a2a3aa22a27a2+a
Find(i) The value of a(ii) P(X
