Let X be a discrete random variable that is the value shown on a single roll of a fair die.(a) What is the expected value of X? Explain the meaning of E(X) in this case.(b) Find the expected value of X².(c) Find the variance of X.(a)(b)(c)

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Answered: Let X be a discrete random variable…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 50E: Earthquakes The proportion of the times in days between major earthquakes in the north-south seismic...

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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?
Earthquakes The proportion of the times in days between major earthquakes in the north-south seismic belt of China is a random variable that is exponentially distributed with a=1/609.5. a. Find the expected number of days and the standard deviation between major earthquakes for this region. b. Find the probability that the time between a major earthquake and the next one is more is than 1 year.

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Let X be a discrete random variable that is the value shown on a single roll of a fair die. (a) What is the expected value of X? Explain the meaning of E(X) in this case. (b) Find the expected value of X². (c) Find the variance of X. (a) (b) (c)