BSc CS Sem 2 BSc CS Semester 2 (2021 2022) May 2022 STATISTICAL METHODS Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Attempt the following 40 marks
   • 1) variable is the variable which can assume finite or countably infinite number of values
   • a) continuous b) discrete
   • 2) Out of the following values, which one is not possible in probability?
   • 3) The cumulative distribution function ranges from
   • 4) For Probability mass function , following condition /conditions satisfied
   • c) P(x;) >0 and P(x;) =1 d) =1
   • 5) For discrete random variable, the expected value
   • a) Dx b) P(x)
   • 6) Following distributions are for discrete random variable
   • a) Binomial distribution and Normal distribution
   • b) Poisson distribution and Normal distribution Binomial distribution and Poisson distribution
   • d) None of these
   • 7) The parameters of binomial distribution are
   • a) nandp b) p and q
   • 8) The parameters of the normal distribution
   • 9). Ina standard normal distribution, the value of mean is
   • a) Equal to zero b) Less than zero
   • c) Greater than zero d) Exactly one
   • 10) Chi-square distribution is
   • 11) In t curve is
   • a) More peaked than normal curve -b) Less peaked than normal curve
   • c) Same as normal curve Difficult to compare with normal curve
   • 12) In case of F -distribution, which of the following statement is true?
   • a) Itis the ratio of two independent sample variance
   • b) It has only one parameter Itis the ratio of two independent population variance
   • d) completely in second quadrant
   • 13) which is tested for the purpose of rejection under the assumption that it is \ true is called
   • 14) Testing Ho: = 25 against H1: #25 leads Right-tailed test d) Difficult to tell
   • 15) The probability associated with committing
   • 16) When testing for serial randomness, we can use
   • 17) Mann-Whitney U test is also called
   • a) Two population b) Three or more Population
   • c) A sample mean to population mean d) Difficult to tell
   • 19) is the process for which there are more than one possible outcomes with
   • a) Probability b) Events
   • 20) Events A and B are Exhaustive events if
2. Q2 Attempt the following (Solve any two ) 10 marks
   • i) Define the following
   • a) Axiomatic definition of Probability
   • b) Classical definition of Probability
   • c) Independent Event li) 5 Indians and 3 Americans stands in a row for photograph randomly. Find the
   • a) two extreme positions are occupied by Indians
   • b) Americans are all together
   • iii) Define Probability density function for continuous random variable Let X be continuous random variable with probability density function f(x) as, Find the value of c
   • iv) Define Cumulative distribution function for discrete random variable. Also state the properties of Cumulative distribution function
3. Q3 Attempt the following (Solve any two ) 10 marks
   • i) IfX is normal variate with mean 30 and variance 25. Find li) Define F distribution. Give all properties of F distribution population IQ scores are normally distributed with mean of 100. One of the School wants to know that whether their students have an IQ greater than population mean. They select a random sample of 15 students and find they have mean IQ of 109 with S.D. of 23. Test the hypothesis at 0.05
   • iv) A discrete random variable X has following probability distribution Find E(X) and Var(X)
4. Q4 Attempt the following (Solve any two) 10 marks
   • i) Differentiate between one-tailed test and two-tailed test
   • ii) A professor of computer science in Mumbai observed that students are very brilliant but they lack of proper writing in university examination. He recorded the number of mistakes done by students, then he gave training of proper writing and recorded the number of mistakes done by same students again Student Number of Number of Using Wilcoxon signed rank test, check whether this difference is significant
   • iii) Explain Run test with suitable example
   • iv) A study was conducted to know the effect of protein diet, Albumin is the most abundant protein in blood, and its concentration in the serum is measured in grams per deciliter (gm/dL). The albumin levels of patients in 3 groups are shown below Using Kruskal Wallis test, Check where there exist Statistically significant difference in serum albumin levels among patients in 3 different diet?
5. Q5 Attempt the following (Solve any one) 5 marks
   • i) In the experiment of pea breeding, following frequencies of seeds were obtained Round and Wrinkled and Round and Wrinkled and Total Theory predicts that the frequency should be in the proportion 9:3:3:] Examine the correspondence between theory and experiment
   • ii) Explain the procedure of testing of hypothesis A and b are two independent events with P(A) = 0.5, P(B) = 0.4 then find

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