BSc CS Sem 2 2022 2023 2023 STATISTICAL MATHODS Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Attempt the following (Any Four) (20M)
   • 1) Two fair dice are rolled. If the sum 10 has appeared, find the probability that one of the
   • 2) Define Probability density function for continuous random variable Let X be continuous random variable with f(x) as, Verify the given function f(x) is probability density function
   • 3) A random variable X has the following probability distribution with p.m.f. p(X)
   • a) Find the value of k
   • b) Find P(X <3)
   • 4) There are 5 boys and 4 girls in managing committee of NSS unit of college. A group of 3 students from this committee is to be send for seminar. Find the probability that the group contains
   • a) At least 2 girls
   • b) Exactly 2 boys
   • 5) Define Cumulative distribution function for continuous random variable Also state the properties of Cumulative distribution function
   • 6) 5 Indians and 3 Americans stands for photograph at random, Find the probability that
   • a) positions are occupied by 2 Indians
   • b) All Americans are together the following (Any Four) (20M)
   • 1) It is observed that if student works hard then the chance of passing an exam is very high i.e. 80%. A random sample of 10 students were selected. What is the probability
   • a) no student will pass
   • b) only 3 students will pass
   • 2) Define F distribution. State the properties of F distribution
   • 3) Let X be a discrete variable with probability density function P(X =x)= = 1,2,3,4,5 . Find E(X) and var(X)
   • 4) The weight of adult goats is normally distributed with mean 25kg and
   • a) Find the probability that the goat’s weight is between 20kg and27kg
   • b) Find the probability that the goat’s weight is more than 29 kg VCD/ Sem II Statistical Mathods 2 Hrs 75 Marks
   • 5) If X is continuous random variable with probability density function Find mean and variance of X
   • 6) An online medicine shop claims that the mean delivery time for medicines is less than 120 minutes with a standard deviation of 30 minutes. Is there enough evidence to support this claim at a 0.05 significance level if 49 orders were examined with a mean of 100 minutes? (use Z test)
2. Q3 Attempt the following (Any Four) (20M)
   • 1) A soap manufacturing company was distributing a particular brand of soap through a large number of retail shops. Before a heavy advertisement campaign, the mean sale per week per shop was 160 dozens. After the campaign, a sample of 25 shops was taken and the mean sale was found to be 167 dozens with S.D. 16: Can you consider the advertisement effective?(use t test)
   • 2) A study is undertaken to know that the impact of proper exercise on blood pressure of students. Total of 15 students were selected and blood pressure recorded before the commencement of exercive program. Then proper exercise was given to these students and again blood pressure was measured after completion of program Following are readings. Check whether Exercise significantly improves the blood
   • 3) Write a short note on One tailed test and Two tailed test
   • 4) Explain Run test with suitable example VCD/ P.Y.B.Sc.CS Sem II Statistical Mathods Hrs 75 Marks
   • 5) manufacturing company want to know the effect of new machinery installed on defects Produced in a lot. A total of 16 machines were chosen includi ng new and old machines. managers were asked to record the defects per lot. The data are shown below Using Mann-witney U test , check whether there is any difference in defects produced by old and new machines
   • 6) A company wants to test whether it’s three salesmen A,B,C has same selling ability The record (in Rs. 1000) during various weeks of last month are recorded in the
3. Q4 Attempt the following (Any Five) (15M)
   • 1) Define the following
   • 2) Explain the procedure of testing of Hypothesis shortly
   • 3) Define Null hypothesis and Alternative Hypothesis with suitable example
   • 4) Define the following terms
   • a) Exhaustive event
   • b) Complementary event
   • c) Sample space
   • 5) State the Properties of Chi-square distribution
   • 6) Differentiate between Non-Parametric test and Parametric test,

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