Question

2. 20 greater tildll 20! Consider the following discrete probability distribution. -25 -15 10 20 PIX=x) 0.35 0.10 0.10 a. Complete the probability distribution. b. Graphically depict the probability distribution and comment on the symmetry of the distribution. C. What is the probability that the random variable X is negative? d. What is the probability that the random variable X is greater than -20? e. What is the probability that the random variable X is less than 20?

Answer 1

Solution:

a. We know that:

T = 1

Let y be the missing probability, therefore, we have:

0.35 +0.10+y+0.10 = 1

0.55+y=1

y = 1-0.55

y = 0.45

Therefore, the complete probability distribution is:

x	-25	-15	10	20
P(X=x)	0.35	0.1	0.45	0.1

b.

0.5 0.45 P(X=x) 0.05 -25 . 15 . 10 . 20

The distribution is not symmetric.

c. The probability that the random variable X is negative is:

P(X = negative) = P(X = -25) + P(X = -15)

-0.35 +0.10 = 0.45

d. The probability that the random variable X is greater than -20 is:

P(X > -20) = P(X = -15) + P(X = 10) + P(X = 20)

= 0.10 +0.45 +0.10

C90-

e. The probability that the random variable X is less than 20 is:

P(X <20) = P(X = -25) + P(X = -15) + P(X = 10)

= 0.35 +0.10 +0.45

  

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