Consider the following discrete probability distribution. x 15 22 34 40 P(X = x) 0.14 0.40 0.26 0.20 a. Is this a valid probability distribution? Yes, because the probabilities add up to 1. No, because the gaps between x values vary. b. What is the probability that the random variable X is less than 40?

(a) Yes, because the probabilities add up to 1.

(b) The probability that X < 40 is 0.80.

Step-by-step explanation:

The probability distribution of the random variable X is:

   x:  15   |   22  |   34   |   40

f (x): 0.14 | 0.40 | 0.26 | 0.20

(a)

The properties of a probability distribution are:

All the probability value are more than 0 and less than 1.

Compute the sum of all the probabilities as follows:

The sum of all probabilities is 1.

Thus, the probability distribution is valid.

(b)

Consider the probability distribution table.

Compute the probability of X < 30 as follows:

P (X < 40) = P (X = 15) + P (X = 22) + P (X = 34)

Thus, the probability that X < 40 is 0.80.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

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im not sure