Section-A
1. Attempt any FIVE parts: 5 i) Distinguish between MUTUALLY and NOT MUTUALLY EXCLUSIVE EVENTS.
ii) Name the Types of RANDOM VARIABLE. iii) If A is a sure event, then what will be the P(A)? iv) If a Coin is tossed TWICE, then what will be the probability of getting 2 HEADS?
v) If P = 0.2, n = 18 in a Binomial Distribution, then what will be Standard Deviation of this DISTRIBUTION. vi) Is a normal distribution LEPTO KURTIC? vii) Is Poisson Distribution a CONTINUOUS DISTRIBUTION? viii) What will be area of Normal Curve for ì ± 3ó ?
Section-B
- a) Show that P(AUB) = P(A) + P(B) – P(An B). 4
- b) What is the PROBABILITY that a leap year selected at random will contain either 53 Thursdays or 53 Fridays? 4
- a) State and prove the multiplication law of probability for two independent events. 4
- b) The odds against a student X solving a business statistics problem are 8 to 6 and odd in favour of the student Y solving the problem are 14 to 16. 4 i) What is the chance that the problem will be solved if they both try independent of each other? ii) What is the probability that none of them is able to solve the problem?
- a) If X and Y are jointly and independently distributed random variables, then show that E(XY) = E(X) E(Y). 4
- b) A player tossed two coins. If two heads show he wins Rs.4. If one head shows he wins Rs.2, but if two tails show he pays Rs.3 as penalty. Calculate the expected value of the game of him. 4
- a) A pair of fair dice is rolled. If x be the difference of the numbers on both dice. Find i) Range of X ii) Probability Distribution of X iii) Distribution Function of X 4
b) A random variable X has the probability density function 4
Kx (9 -x^{2}) for0 = x = 3
f (x) =
0 elsewhere
Find the value of K, the mean and standard deviation of X.
- a) Find the moment generating function of Poisson Distribution. 4
- b) If hens of a certain breed lay eggs on 5 days a week on an average, find how many days during a season of 100 days a poultry keeper with 5 hens of this breed, will expect to receive at least 4 eggs. 4
- a) Show that the Hypergeometric is a probability distribution. 4 b) Ten cans of the same size have lost their labels. It is known that five contain tomatoes and five contain
- corn. If five cans are selected at random, what is the probability that: 4 i) All contain tomatoes.ii) At least one contain tomatoes.
- a) Show that the normal curve has points of inflection are equidistant from the mean. 4
b) The length of life for working washing machines is approximately normally distributed with a mean of 3.5 years and a standard deviation of 1.0 year. If this type of working machine is guaranteed for 12 months what percentages of the sales will require replacement? 4
*** B.A/B.Sc – I (09/A) xxxvi ***