College Majors Table 4 shows the probable field of study for 1500 freshman males and 1000 freshman females. Find the probability that a freshman selected at random a. intends to major in business. b. is female. c. is a female intending to major in business. d. is male, given that the freshman intends to major in social science. e. intends to major in social science, given that the freshman is female. Table 4 Business Social Science Other Total Male Female Total 260 102 362 122 130 252 1118 768 1886 1500 1000 2500 Source: www.heri.ucla.edu
College Majors Table 4 shows the probable field of study for 1500 freshman males and 1000 freshman females. Find the probability that a freshman selected at random a. intends to major in business. b. is female. c. is a female intending to major in business. d. is male, given that the freshman intends to major in social science. e. intends to major in social science, given that the freshman is female. Table 4 Business Social Science Other Total Male Female Total 260 102 362 122 130 252 1118 768 1886 1500 1000 2500 Source: www.heri.ucla.edu
Solution Summary: The author calculates the probability that a randomly selected freshman wants to major in business with the help of the following table.
College Majors Table 4 shows the probable field of study for 1500 freshman males and 1000 freshman females. Find the probability that a freshman selected at random
a. intends to major in business.
b. is female.
c. is a female intending to major in business.
d. is male, given that the freshman intends to major in social science.
e. intends to major in social science, given that the freshman is female.
A random variable X takes values 0 and 1 with probabilities q and p, respectively, with q+p=1. find the moment generating function of X and show that all the moments about the origin equal p. (Note- Please include as much detailed solution/steps in the solution to understand, Thank you!)
1 (Expected Shortfall)
Suppose the price of an asset Pt follows a normal random walk, i.e., Pt =
Po+r₁ + ... + rt with r₁, r2,... being IID N(μ, o²).
Po+r1+.
⚫ Suppose the VaR of rt is VaRq(rt) at level q, find the VaR of the price
in T days, i.e., VaRq(Pt – Pt–T).
-
• If ESq(rt) = A, find ES₁(Pt – Pt–T).
2 (Normal Distribution)
Let rt be a log return. Suppose that r₁, 2, ... are IID N(0.06, 0.47).
What is the distribution of rt (4) = rt + rt-1 + rt-2 + rt-3?
What is P(rt (4) < 2)?
What is the covariance between r2(2) = 1 + 12 and 13(2) = r² + 13?
• What is the conditional distribution of r₁(3) = rt + rt-1 + rt-2 given
rt-2 = 0.6?
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