Name of the Organization : Board of School Education West Bengal
Name of the Exam : Higher Secondary
Subject : Statistics Theory)
Document Type : Model Question Paper
Website : http://www.wbsed.gov.in/welcome.html
Download Sample/Model Question Paper : https://www.pdfquestion.in/uploads/11302-statistics.pdf
Statistics Theory Model Question Paper :
1. i) Write down the result of (1 e x ) dx d – -?
OR,
If M is the mode of a discrete probability distribution with mass function f then f(x) = ………….. at x = M.
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ii)If two variables are proportional then they do not have any correlation. (Write true or false)
iii) In case of ranking some individuals with respect to a characteristic tied ranks may occur. (Write true or false)
OR, Two ranks of an individual must be equal when some individuals are ranked with respect to two attributes. (Write true or false)
iv) To study the trend of a time-series one needs to take
(a) only one observation
(b) two observations
(c) only daily observations
(d) observations for a sufficiently long time (Write the correct answer)
v) A random variable X is such that P(X = 1) = P(X = 0) = 1/2 . What is the value of P(X > 0) ?
vi) If a discrete variable assumes values 5, 6, 7, 8, 9 and 10 with equal probabilities then its probability mass function is given by 0, otherwise …………., if, x 5,6,7,8,9,10 f(x) (Fill in the blank)
OR,
In case of a continuous random variable X P(X = 2.22) = …………………. (Fill in the blank)
vii) For a binomial variable X E(X) < Var (X). (Write true or false)
viii) If the parameter of a Poisson distribution is 7.83 then its mode is …………… (Fill in the blank)
ix) If a digit is taken from a random number series, the probability that it is 9 and the probability that it is not 9 are not equal. (Write true or false)
OR,
Can any digit repeat in a random number series ?
x) If the observed values of a sample are given, the value of a statistic becomes fixed.
GROUP – B :
2. i) When only two attributes A and B having two forms each are considered, how are the marginal frequencies and the total frequency related ?
ii) Define bivariate data with a suitable example.
OR,
When are two variables said to be positively correlated ?
iii) Show the case when the value of Spearman’s rank correlation coefficient will be +1.
OR,
What do you mean by rank correlation ?
iv) If for a binomial distribution m = 10 and p = 13/5 then what is the value of the coefficient of variation ?
OR,
If for a binomial distribution the expected value is 4 and variance is 3, what are the values of its parameters ?
v) Show that a normal distribution is symmetric about its mean.
GROUP – C :
Find the first order raw moment of the probability distribution having density function, given by f(x) ={e – X/e}
ii) In the 2 x 2 ease of two attributes A and B discuss the cases of association. OR, Draw scatter diagrams in cases of perfect correlation between two variables.
iii) If the bases and scales of two correlated variables are changed, determine the effect on correlation coefficient. OR, If two variables x1 and x2 have a common variance and correlation coefficient r= 0, express r in terms of q so that x1 + 2×2 and x1 + x2 (q = 1) become uncorrelated.
Ans: Consider the pair of values (x1, y1), (x2, y2), ….. (xn, yn) on the variables (x, y) Hence numerical value of the correlation coefficient remains unaltered with the change of base & scale.
iv) Derive the two normal equations in case of obtaining a linear regression line on the basis of bivariate data.
OR
If the normal equations are given for obtaining a linear regression line thendetermine the regression line.
v) Describe the method of trend determination by the moving average method when the period-length is an even integer.
OR,
State the disadvantages of determining trend by the method of moving averages.
vi) Give the definition of a probability mass function of a random variable X and express P(X = x | X < x0) by using such function.
OR
If an unbiased coin is tossed thrice, find the probability distribution of the number of tails.
vii) Determine the median of a uniform (a, ß) distribution.
OR
Determine the variance of a uniform (a, ß) distribution.
viii)If a Poisson variable X is such that 2P = (X = 5) = P(X = 6) then what is the value of P (X > 0) OR, If a binomial (10, p) variable X is such that P(X = 5) = P(X = 6) then what is the value of p ?
ix) In case of fitting a binomial distribution to a frequency distribution of a variable X, how will you estimate p and use it to find out an estimate of P(X = x) ?
x) Describe the process of selecting 3 boys from a group of 10 boys by using a random number series.
OR
“In a sample survey more accurate result is obtained and sampling error may be gauged”. Explain
xi) Give the definition of minimum variance unbiased estimator. Show that if f be the number of successes out of n Bernoulli trials with success probability p then f/n is unbiased for p.
GROUP – D :
4. i) For a Poisson (y) distribution the 2nd, 3rd and 4th central moments are µ2 =y , µ3 = y++2 and µ4 = 3y2 + y respectively. Use these to measure skewness and kurtosis of the distribution. Hence comment on the skewness and kurtosis of the distribution.
OR
Given that for a normal (µ, s2) distribution the mean is 65.5 inches and P(Z > 60.5) 0.9. Find the interval (µ – 3s, µ + 3s)
ii) If there independent estimators T1, T2 and T3 be unbiased for a parameter 0 and their variances are in the ratio 2 : 1 : 3 then which one of the following estimators would you prefer most for ? and why ?