BSc Statistics SEM II 2021 2022 2022 STATISTICS II Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Tick mark the correct option (2 mks each) IA random variable is uniformly distributed over the interval 2 to 10. It’s variance will be,
   • 2) Arandom variable is uniformly distributed over the interval (3,12).It’s variance will be,
   • 3) Arandom variable is uniformly distributed over the interval (8,15). It’s variance will be,
   • 4). The mean of continuous uniform Distribution is
   • 5) The p.d.f. of uniform X~U(0, 20) then find the P(X<5)?
   • 7) The variance of uniform distribution is given by
   • 8) In the continuous uniform distribution (a)mean=median (b) mean>median
   • 9) The distribution function F(x) is equal to
   • (b)PXSx (c)PX=x (d)AIl the above
   • 10)A range of values of within which the population parameter is expected to occur is called
   • c)Confidence limits d)Level of significance
   • 11)A formula or The Rules are used for estimating the parameter is called
   • d)Interval Estimate
   • 12)If = 0.90 then the value is
   • 13)In hypothesis testing, a Type Il error
   • a)The null hypothesis is not rejected when the null hypothesis is true
   • b)The null hypothesis is rejected when the null hypothesis Is true
   • c)The null hypothesis is not rejected when the alternative hypothesis is true
   • d)The null hypothesis is rejected when the alternative hypothesis is true
   • 14)Null and alternative hypotheses are statements about:
   • c)sample statistics. d)either population parameters or sample statistics
   • 15)Central Limit Theorem (CLT) states that the distribution of sample mean tends to a of the distribution of population
   • 16)A is an assertion about the value of a population parameter
   • a) Null hypothesis
   • b) Alternative hypothesis
   • c) Simple hypothesis
   • d) Composite hypothesis
   • 17) If Hy: p = > against H; then it is
   • a) Simple against composite hypothesis
   • b) Simple against simple hypothesis
   • c) Composite against composite hypothesis
   • d) Composite against simple hypothesis
   • 18) The formula for finding standard error (S.E.) of sampling distribution of means is f(x) is probability density function ( p.d.f) of continuous random variable X then where S is a sample space
   • 20)The cumulative distribution function (cdf)for continuous random variable F(x) is 4 any two random variable X,Y
   • 22)The median (F(M)) for cumulative frequency
   • 23) A variable that can assume any possible value between two points iscalled
   • d)Random variable
   • 24) A formula or equation used to represent the probability’ distribution of a continuous random
   • 25)A probability density function is represented
   • a) table. b) graph. c) mathematical equations d) both b and c
2. Q2 Attempt any three of the following (5 MKS each) whether following function is p.d.f or not
   • 2)Let X be a continuous random variable with p.d.f given by X be a continuous random variable with p.d.f given by
   • 4)The density function of X is
3. Q3 Attempt any three of the following (5 MKS each)
   • 1)Define uniform distribution over an interval (a, b). Find it’s (ii)variance
   • 2) An government luxury bus from Mumbai to Pune run every 20 minutes. The waiting time is uniform over the interval (0,20)
   • (a) What is it’s
   • (b)What is the probability that passenger have to wait at least 10 minutes?
   • 3)State and prove lack of memory (memoryless) property of exponential distribution
   • 4) If X~U(a,2a), find the value of ‘a’ such that P(|X|>5)
4. Q4 Attempt any three of the following (5 MKS each)
   • 1)Define Estimation and Explain the types of estimation is found that for those who have lost weight, 31 % believed the most effective strategy involved exercise. What is the probability that from random sample of 300 persons the sample proportion falls between 29% and 33%?
   • 3)In a metropolitan area, the concentration of cadmium (Cd) in leaf lettuce was measured in 60 representative gardens where sewage sludge was used as fertilizer. was found that the average content of Cd. in selected sample was 18 mg/kg of dry weight with S.D. of 9. Is there evidence that the mean concentration of Cd is higher than 12.If required obtain 95% confidence interval
   • 4)A sample of size 100 is drawn from Poisson population with mean 4 .Find approximate probability that sum of 100 such observations is atleast 430
5. Q5 Attempt any one of the following (5 MKS each)
   • 1)A spinner that could take on any value has density function
   • 2)A random variable X has an exponential distribution with mean 5. Find
   • 3)Define following i) Population ii) Sample iii) Parameter iv) statistic v) Sampling Error

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