Question

Hello please Use the following discrete probability distribution below to answer the following questions:

                                      X          p(x)

1          0.16

2          0.17

3          0.33

4          0.16

5          0.10

6 UNKNOWN

1. a What is the probability that x = 6?

                        P(6) = 0.08        P(6) = 0.18        P(6) = 0.24        P(6) = 0.35

1.b)    What is the mean of the probability distribution?

                        µ = 2.92            µ = 3.11            µ = 3.51            µ = 4.00

           

1.c)         What is the standard deviation?

                        σ = 0.98            σ = 1.22            σ = 1.44            σ = 1.96

Now what if Bob invests in three stocks. His return in dollars and the probability for each return is listed below.

                        Stock A             $300                 p= 0.50

                        Stock B             $600                 p= 0.30

                        Stock C             $800                 p= 0.20

            What is Bob’s expected return for the stocks in his portfolio?

1. $360           b) $400             c) $450             d) $490

Answer 1

1a) P(X = 6) is computed by using the property that the sum of all probabilities across the X range should be 1. Therefore we get here:
P(X = 6) = 1 - 0.16 - 0.17 - 0.33 - 0.16 - 0.1 = 0.08
Therefore P(6) = 0.08 is the required probability here.

1b) The mean of the probability distribution here is computed as:
Mean = 1*0.16 + 2*0.17 + 3*0.33 + 4*0.16 + 5*0.1 + 6*0.08 = 3.11
Therefore b) 3.11 is the required mean here.

1c) The second moment of X is first computed here as:
E(X²) = 1²*0.16 + 2²*0.17 + 3²*0.33 + 4²*0.16 + 5²*0.1 + 6²*0.08 = 11.75

Therefore the standard deviation is computed here as:

Therefore 1.44 is the required standard deviation here.

The expected return is computed as the sum product of returns with the probability:

= 300*0.5 + 600*0.3 + 800*0.2

= 490

Therefore d) 490 is the expected return here.