06-10-2011, 03:31 PM
Spring 2011 (Total Marks 30)
Assignment 3 (Lessons 23-30)
Question 1: Marks:2+3+3+3+4=15
a) If Z is a standard normal random variable with mean 0 and variance 1, then find the lower quartile.
b) A random variable ‘x’ is said to be uniformly distributed such that
(i) Write down the density function of ‘x’
(ii) Prove that total area between the given limits is unity.
c) What is the probability that a poker hand of 5 cards contain exactly 1 ace?
d) A certain type of storage battery lasts on the average 3.0 years, with a standard deviation of 0.5 year. Assuming that the battery lives are normally distributed, find the probability that a given battery will last less than 2.3 years.
e) The incident of occupational disease is such that the workers have 20 percent chance of suffering from it. What is the probability that out of six more than 4 workers will come in contact of the disease?
Question 2: Marks:3+3+4+5=15
a) The Probability distribution of X is given below:
Compute,
i) P(x=2)
ii) E(X)
X
0 1 2 3 4
P(X)
b) The p. d. f. of a random variable is given
f(x) = (2x-1) 1
0 Elsewhere
Calculate P(X<1.5).
c) The given information is obtained from a joint distribution of X and Y. Calculate Correlation coefficient () between X and Y.
d) Find the value of A, such that the function f(x, y) is a density function.
Assignment 3 (Lessons 23-30)
Question 1: Marks:2+3+3+3+4=15
a) If Z is a standard normal random variable with mean 0 and variance 1, then find the lower quartile.
b) A random variable ‘x’ is said to be uniformly distributed such that
(i) Write down the density function of ‘x’
(ii) Prove that total area between the given limits is unity.
c) What is the probability that a poker hand of 5 cards contain exactly 1 ace?
d) A certain type of storage battery lasts on the average 3.0 years, with a standard deviation of 0.5 year. Assuming that the battery lives are normally distributed, find the probability that a given battery will last less than 2.3 years.
e) The incident of occupational disease is such that the workers have 20 percent chance of suffering from it. What is the probability that out of six more than 4 workers will come in contact of the disease?
Question 2: Marks:3+3+4+5=15
a) The Probability distribution of X is given below:
Compute,
i) P(x=2)
ii) E(X)
X
0 1 2 3 4
P(X)
b) The p. d. f. of a random variable is given
f(x) = (2x-1) 1
0 Elsewhere
Calculate P(X<1.5).
c) The given information is obtained from a joint distribution of X and Y. Calculate Correlation coefficient () between X and Y.
d) Find the value of A, such that the function f(x, y) is a density function.
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