Consider a share that is modelled by a binomial random variable. The probability that the share increases in value by 20¢ in one month is 0.6. The probability that it decreases in value by 20¢ in one month is 0.4. The share is held for 5 months then sold. Let X denote the number of increases in the price of the share over the 5 months. В (п, (a) What is n and p if X∼B(n,p)? (b) Find E(X)andσ(X). (c) Let Y be the random variable which models the change in share price. Then ҮҮ−0.2X−0.2(n−X) because 0.2X is the total increase in share price and 0.2(n−X) is the total decrease in share price. Simplify the expression for Y in terms of X. Then using (b), find E(Y) and σ(Y).

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Consider a share that is modelled by a binomial random variable. The probability that the share increases in value by 20¢ in one month is 0.6. The probability that it decreases in value by 20¢ in one month is 0.4. The share is held for 5 months then sold. Let X denote the number of increases in the price of the share over the 5 months. В (п,   (a) What is n and p if X∼B(n,p)?  (b) Find E(X)andσ(X).  (c) Let Y be the random variable which models the change in share price. Then ҮҮ−0.2X−0.2(n−X) because 0.2X is the total increase in share price and 0.2(n−X) is the total decrease in share price. Simplify the expression for Y in terms of X. Then using (b), find E(Y) and σ(Y).

Natalie Yamamoto · Accepted Answer

Step 1  Part a:  Let the random variable X denote the number of increase in the price of the share over the 5 months.  Thus, n=total number of months=5  p=the probability that the share increases in value by 20 in one month  =0.6  q=the probability that the share decreases by value 20 in one month  =0.4  Thus, X∼B(5,0.6)  Part b:  We know the mean and variance of binomial distribution are given by,  Mean=E(X)=np=5×0.6=3 (1)  Variance =V(X)=npq=5×0.6×0.4=1.2 (2)  Thus,   σ(X)=V(X)=1.2=1.0954  Step 2  The random variable y is defined as,  Y=0.2X−0.2(n−X)  =0.2X−0.2n+0.2X  =0.4X−0.2(5)  =0.4X−1.0  Thus, we have mean and variance of random variable Y as,  Mean (Y)=E(Y)=E(0.4X−1.0)  =0.4E(X)−1.0  =0.4×3−1.0 (From (1))  =0.2  Variance (Y)=V(Y)=V(0.4X−1.0)  =0.42V(X)  =0.16×1.2 (Form (2))  =0.192  Thus, σ(Y)=V(Y)=0.192=0.4382

soanooooo40 · Accepted Answer

Answer:  The price-to-earnings ratio (PE ratio) of a stock is given by  R(x, y)=xy  where  denotes the price per share of the stock and  denotes the earnings per share. Estimate the change in the PE ratio of a stock if its price increases from $60 share to $62 share while its earnings decrease from $4 share to $3.80 share.

Consider a share that is modelled by a binomial random varia

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