Question

Three tables listed below show random variables and their probabilities. However, only one of these is actually a probability distribution.

Table 1: X    P(X) Table 2: X    P(X)              Table 3:   X    P(X)

               25     0.1                           25     -0.6                        25        0.5

              50      0.7                           50    0.2                            50      0.3

              75     0.2                            15    0.1                            75       0.1

              100   0.4                            100    0.1                          100    0.1

a. Which of the above tables is a probability distribution? b.Using the correct probability distribution, find the probability that x is 1. Exactly 75 = 2. No more than 50= 3. More than 25= c) Compute the mean, variance, and standard deviation of this distribution 1. Mean = 2. Variance= 3. Standard deviation =

Answer 1

a.

Table 1 is not a correct probability distribution as the sum of probabilities of the values under the random variable X exceeds ,which is absurd.

Table 2 also does not give a correct probability distribution , because here , which is impossible.

Under Table 3, the probabilities are positive and add up to 1,too. So, it is the correct probability distribution.

b.

c.

Now,

Mean=

Variance =

Then,

Therfore,

Standard Deviation=