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Homework answers / question archive / X is a discrete random variable representing the profit for a given investment
X is a discrete random variable representing the profit for a given investment. The probability distribution of X is given as: P(X = x) 0.20 -1 0.30 1 2 0.20 (You must find the missing value to answer this question). What is the variance of X? Select one: O A. 2.2 O B. 1 C. 1.4 D.O E. None of those listed.
5. If the expected inflation rate was 2.5%, the ex-ante real interest rate was 4.0%, and the actual inflation rate turned out to be 3.2%, then the ex-post real interest rate equals A) 1.7%. B) 3.2%. C) 3.3%. D) 4.7%.
The sum of the probability is 1.
=> P (X = -2) + P (X = -1) + P (X = 1) + P (X = 2) = 1
=> 0.20 + 0.30 + P (X = 1) + 0.20 = 1
=> 0.70 + P (X = 1) = 1
=> P (X = 1) = 1 - 0.70
=> P (X = 1) = 0.30
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E(X) = Σ (X . P(X) )
=> E(X) = (-2 * 0.20) + (-1 * 0.30) + (1 * 0.30) + (2 * 0.20)
=> E(X) = (-0.40) + (-0.30) + (0.30) + (0.40)
=> E(X) = 0
The expected value of X is 0.
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Var(X) = E(X2) - [E(X)]2
First we have to find E(X2)
E(X2) = Σ (X2 . P(X) )
=> E(X2) = (-22 * 0.20) + (-12 * 0.30) + (12 * 0.30) + (22 * 0.20)
=> E(X2) = (4* 0.20) + (1 * 0.30) + (1 * 0.30) + (4 * 0.20)
=> E(X2) = (0.80) + (0.30) + (0.30) + (0.80)
=> E(X2) = 2.20
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Var(X) = E(X2) - [(E(X)]2
=> Var(X) = 2.20 - (0)2
=> Var(X) = 2.20 - 0
=> Var(X) = 2.20
The variance of X is 2.20
Answer: Option (A)
Ex-ante real interest rate is calculated by taking the expected value of inflation rates in the economy. It is calculated as following:
Ex-ante Real interest rate= Nominal Rate of interest - Expected inflation
We have, Ex-ante Real interest rate= 4%
Expected inflation= 2.5%
Nominal rate of interest= Ex-ante Real interest rate + Expected inflation
= 4 + 2.5
= 6.5%
Now, Ex-post real interest rate can be calculated by taking the actual level of inflation:
Ex-post Real interest rate= Nominal rate of interest - Actual Inflation
We have, Nominal rate of interest = 6.5%(calculated above)
Actual inflation= 3.2%
Ex-post real interest rate= 6.5 - 3.2
= 3.3%
So, the correct option is c) 3.3%.
