RAN-2235
F.Y.B.A. (External) Examination
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March / April - 2019
Statistics Higher Paper : 1
? : / Instructions
? ? ? ? ? ? ? ?.
Fill up strictly the details of signs on your answer book
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Name of the Examination:
F.Y.B.A. (External)
Name of the Subject:
Statistics Higher Paper : 1
Subject Code No.: 2 2 3 5
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(?) ? ? ? ? ? ? ? ?.
(?) ? (? ?) ? ? ? ?.
(?) ? ? ? ? ?.
?. 1 (?) ? ? ? ? ? ? ?.
(?) ? f(x) = | x² - ½ | ? ? f(-4) - f(2)/2 ?.
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(?) ? ? ?.
(1) lim x?0 2x³- 5x² + 4x/3x³ + 2x²
(2) lim x?3 x³ + x - 12/4x + 3
(?) ? ? lim x?-1 2x²+ 1 ? ? ?.
?
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(?) ?.
(1) ? ?
(2) ? ?
(3) ? ? ? ?
(?) f(d) = 30 – 2d – d² ? d = 0, 1, 2, 3, 4 ? ? ? ?.
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RAN-2235 ] [1] [ P.T.O. ]
(?) ? ? ?.
(1) lim x?2 v(x²-4)/(x-2)
(2) lim x?-1 x³ + 1/x²-1
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(?) ? ? ?. ? ? ? ? ? ?.
?.2 (?) ? ? ?. ? ? ? ?.
(?) ? ?.
(1) Y = X (1-1/X)(1-1/(X-1)) (2) Y = 3/4-X
(?) ? ? ? ? ? ? ? ? ? ? ? ?.
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D=50-8p/7 , S=10+2p/3
(?) ? Y = x² ? ? ? ? ?.
?
(?) ?.
(1) ? ?
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(2) ? ? ? ? ? ? ?
(?) ? ? ? ? ? ? R = 20X – 4X² ? ? ? C = 4X ?. ? ? ? ? ? ? ? ? ? ? ?.
(?) ? ?.
(1) Y = log x/X (2) Y = X³ - 3X² - 9X ? ? ?
?. 3 (?) ? ? ?. ? ? ? nCr + nCr-1 = n+1Cr.
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(?) 4 ? ? 3 ? ? ? ? ? ? ? ? ? 2 ? ? ? ? ?
(?) ? nPr = 360 ? nCr = 15 ? ? n ? r ?.
(?) 4, 5, 7, 6, 2, 8, 1 ? ? ? 3 ? ? ? ? ? ? ? ? ? ?
?
(?) ? ? ? ? ? ? n Pr= n!/(n-r)!
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RAN-2235 ] [2] [ Contd.
(?) ? ? ? ? ?. ? A ? ? B ? ? 4 ? 3 ? ?. ? ? ? ? 1 ? ? ? 5 ? ? ? ? ? ? ? ? ? ? ? ? ? ?
(?) ? 10C3 + 2(10C4) + 10C5 = 12Cx ? ? x ?.
(?) ? ? ? 3 ?, 4 ? ? 5 ? ? ?. ? ? ? ? ?
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?. 4 (?) ? ? ? ?. ? ? ?.
(?) ? ? ? ? ? A, B ? C ? ? ?. ? ? ? ? ? ? ? ? 20% ? A ? ?, 16% B ? ?, 14% C ? ?, 8% A ? B ? ?, 5% A ? C ? ?, 4% B ? C ? ? ? 2% A, B ? C ? ? ?. ? ? ? ? ? ? ? ? ? ? ?.
(?) ? P(A) = 1/3,P(B) = 1/4, P(AnB) = 1/6 ? ? P (A ? B) ? P (A / B) ?.
(?) ? ? ? ? ? ? 53 ? ? ? ?.
?
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(?) ?.
(1) ? ? (2) ? ? (3) ? ? ?.
(?) 52 ? 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?.
(?) ? ? 5 ? ? ? ? ?. ? 3 ? ? ? ? 1/12 ?. ? ? ? ? ? ?.
(?) ? P(A) = 2/3, P (B) = 1/2, P(AnB) = 4/15 ? ? P(A n B') = 1/6 ?.
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?.5 (?) ? ? ? ? ?.
(?) 4, 6, 8, 10 ? 12 ? ? “7” ? ? ? ? ? ? ?. ? ? ? ? ? ? ? ? ?.
RAN-2235 ] [3] [ P.T.O. ]
(?) ? ? x ? ? ? ? ? ?. ? ? ? ? X ? ? ? ? ? ?.
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X 0 1 2 3 4 5
P(X) K 0.2 0.1 K 0.05 0.05
?
?. 5 (?) ? ? ?. ? ? ? ?.
(?) ? ? ? X = 18 ? Y ? ? ?.
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X 14 15 17 20 22
Y 8 30 35 42 50
(?) ? ? ? ? ? ?.
X 11 12 13 14 15 16 17 18
Y 8 10 13 ? 24 30 36 45
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ENGLISH VERSION
Instructions:
(1) Figures to the right indicates full marks of the questions.
(2) Simple calculator (without programmable) can be used.
(3) Graph and statistical table can be provided on request.
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Q1. (a) Explain demand and supply function with illustration.
(b) If f(x) = |x²- ½ | then find f(-4) - f(2)/f(-2)
(c) Find the values of the following.
(1) lim x?0 2x³- 5x² + 4x/3x³ + 2x² - 2x
(2) lim x?3 x³ + x - 12/x²- 4x + 3
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(d) Obtain the value of lim x?-1 2x² + 1 with the help of table
OR
RAN-2235 ] [4] [ Contd.
(a) Explain.
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(1) Linear function
(2) Range of a function
(3) Domain and Codomain of a function
(b) Draw the graph for the function f(d) = 30 - 2d - d² for considering the values d = 0, 1, 2, 3, 4
(c) Find the values of the following.
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(1) lim x?2 x²-4/x-2
(2) lim x?-1 x³ + 1/x²-1
(d) Define limit. State the any two rules of a limit
Q2. (a) Define differentiation. State the uses of differentiation in economics.
(b) Obtain differentiation.
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(1) Y = x(1-1/X)(1-1/(X-1)) (2) Y = 3/4-X
(c) Find the equilibrium price using the below given demand and supply function.
D=50-8p/7 , S=10+2p/3
(d) Obtain the differentiation Y = x² of the following function with the help of definition.
OR
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(a) Explain.
(1) Elasticity of demand
(2) Total cost function and Average cost function.
(b) For a commodity total revenue function R - 20X - 4X² and cost functions C = 4X. How many units produced for maximum profit? Also find maximum profit.
(c) Obtain differentiation.
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(1) Y = log x/X (2) Y = X³ - 3X² - 9X for minimum value.
RAN-2235 ] [5] [ P.T.O. ]
Q3. (a) Define combination. Prove that nCr + nCr-1 = n+1Cr.
(b) In how many ways can 4 boys and 3 girls stand in a row so that no two girls are together?
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(c) Find n and r if nPr = 360 and nCr = 15.
(d) How many 3 digited numbers can be formed using the digits 4, 5, 7, 6, 2, 8, 1 only One time? How many of them are odd numbers?
OR
(a) In usual notations prove that nPr= n!/(n-r)!
(b) A question paper which is divided into two sectionconsisting of 4 and 3 questions respectively. Answer 5 questions selecting at least one questions from each section. In how many ways can a candidate select questions?
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(c) If 10C3 + 2(10C4) + 10C5 = 12Cx, find x.
(d) There are 3 English, 4 Hindi, and 5 Gujarati books on a shelf. How many total arrangements are possible?
Q4. (a) Give a definition of mathematical probability. State its limitations?
(b) In a city three daily new papers A, B, C are published. It was found from a survey that 20% read A, 16% read B, 14% read C, 8% read both A and B, 5% read both A and C, 4% read both B and C and 2% read all the three. Calculate the percentage of people who read at least one of them.
(c) If P(A) = 1/3,P(B)= 1/4, P(AnB)= 1/6 then find P (A ? B) and P(A/B)
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(d) What is the probability of getting 53 Sundays in a non leap year?
OR
(a) Explain.
(1) Sample space (2) Exhaustive events (3) Mutually exclusive events
(b) Two cards are drawn from a pack of 52 cards. What is the probability that there is one king and one queen?
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(c) There are 5 boys and certain girls in a group. Three boys are selected from that group whose probability is 1/2, then find number of girls in that group.
RAN-2235 ] [6] [ Contd.
(d) If P(A) = 2/3, P (B) = 1/2, P(AnB)= 4/15 then find P(AnB') = 1/6
Q 5. (a) State the assumptions and uses of interpolation.
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(b) Find first three moments about "7" using the observations 4, 6, 8, 10, 12. From these Raw moments, obtain first three central moments.
(c) The probability distribution of a random variable X is given below. From that find the Expected value and variance of variable X.
X 0 1 2 3 4 5
P(X) K 0.2 0.1 K 0.05 0.05
OR
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(a) Explain mathematical expectation. Write characteristics of a mathematical expectation.
(b) Estimate Y for X = 18 from the following data.
X 14 15 17 20 22
Y 8 30 35 42 50
(c) Find missing data from the following table.
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X 11 12 13 14 15 16 17 18
Y 8 10 13 ? 24 30 36 45
RAN-2235 ] [7] [180]
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