BSc Sem III 2023 2024 2024 STATISTICS I Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Answer the following questions
   • a) Correct the following if necessary: (10M)
   • i. Binomial distribution is continue
   • ii. The mean of binomial distribution depends on n only ili. For Poisson distribution discrete distribution
   • iv. Hypergeometric distribution has two parameters
   • v. Coefficient of correlation lies between -1 to 0
   • i. Define Characteristic Function of r.v.y li. State p.m.f of poisson distribution
   • iii. State p.d.f of normal distribution
   • iv. Define covariance between two random variables
   • v. State property of correlation coefficient
2. Q2 Attempt anv TWO (20M)
   • a) Define C.G.F and Write properties of it also prove any one peoperty
   • b) i) Ifar.v.X follows binomial distribution with parameter (n,p) obtain expression for its
   • M.G.F hence Evaluate its mean and variance
   • i) Obtain M.G.F hence find mean and variance Attempt any TWO (20M)
   • a) State the P.m.f of Negative Binomial distribution and hence Obtain its mean and
   • b) i) Obtain the P.m.f of Truncated Poissoa distribution truncated at 0 li) Define Seometric Distribution State its M.G.F and C.G.F VCD\ SYB.Sc (MS) SEM-III Probability Distribution HRS-3 MARKS-100
   • c) State the of Poisson distribution, Obtuin its mean and variance using the M.G.F
3. Q4 Attempt any TWO (20M)
   • a) Define joint probability mass function and cumulative distribution function of bivariate discrete r.v’s X and Y. State all properties of cumulative distribution function The joint p.m.f of (X,Y) is given below If a random follows uniform distribution over the range (0, 1)
4. Q5 Attempt any TWO (20M)
   • a) i) Prove that for large n binomial distribution tends to Poisson distribution
   • ii) Write down the properties of covariance
   • b) Write down the properties of covariance. Evaluate V(aX+bY)
   • c) i) Describe Correlation Coefficient, State its Properties
   • ii) Obtain the m.g.f of binomial distribution

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