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A stock can earn a return of 2%, 20%, or 8%. The stock’s distribution is known, and states that there is a 30% probability of the stock earning a return of 2%, a 36% probability of the stock earning a return of 20%, and a 34% probability of stock earning a return of 8%. What is the variance of the stock’s return?Select one: a. .0056 b. .0923 c. .0061 d. .078 e. .0748

Respuesta :

Answer:

option (a) 0.0056

Explanation:

Data provided in the question:

Return that can be earned :   2%      20%       8%

Probability of returns :          30%      36%       34%

Now,

Average return, m = [tex]\frac{2\% + 20\% + 8\%}{3}[/tex] = 10%

Return (X)     P(X)     X - m                    ( X - m )²     ( X - m )² × P(X)

     2%          30%    -8% = -0.08           0.0064               0.00192

     20%        36%    10% = -0.10           0.01                       0.0036

     8%          34%    -2% = -0.02           0.0004               0.000136

Thus,

Variance of the stock’s return = ∑ ( ( X - m )² × P(X) )

= 0.00192 + 0.0036 + 0.000136

= 0.005656 ≈ 0.0056

Hence,

The correct answer is option (a) 0.0056

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