Q.2 bivarate one 3016--(P-4)(Q-9)(20)Marks inEconomicsMarks inMaths(4)78 36 98 25 75 82 90 62 65 3981 51 91 60 68 62 86 58 53 47(f) Find the least value of r in a sample of 18 pairs ofobservations from a bivariate normal population,significant at 5% level of significance.(a) There are two bags. The first bag contains 10 whiteand 3 black balls and second bag contains 3 whiteand 5 black balls. Two balls are drawn at random5°from the first bag and put into second bag. Then aball is drawn from second bag. Find the 13probability that the ball drawn is a white ball.(b) If X and Y are two independent random variables,then show that:4/6Var (X+Y) = Var (X) + Var (Y)(a) For a random variable X with mean μ = 10 andvariance o² = 4, apply Chebyshev's inequality tocalculate :-(P-4)(Q-9)(20)(i) P(5 < X < 15)(ii) P(|X-10| ≥3)(iii) P(|X-10| <3)b) A car hire firm has two cars, which it hires out dayby day. The number of demands for a car on eachday is distributed as a Poisson variate with mean1.5. Calculate the proportion of days on which :0.2231(i) neither car is used(ii) some demand is refused 1912625(2)...

Given: V(X+Y) = V(X) + V(Y) X and Y are independent random variables.

Answered: ) If X and Y are two independent random…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.6: Higher-degree Polynomials And Rational Functions

Problem 5E: Population Genetics In the study of population genetics, an important measure of inbreeding is the...

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Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?

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