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"Determine whether or not the distribution is a discrete probability distribution and select the reason why or why not.

x −3 1 5

P(X=x) 1/2 5/8 3/4

Answer First, decide whether the distribution is a discrete probability distribution, then select the reason for making this decision. Decide Reason"

(Yes / No)

(a) Since the probabilities lie inclusively between 0 and 1 and the sum of the probabilities is equal to 1. (b) Since at least one of the probability values is greater than 1 or less than 0. (c) Since the sum of the probabilities is not equal to 1. (d) Since the sum of the probabilities is equal to 1. (e) Since the probabilities tie inclusively between 0 and 1.

Respuesta :

Answer:

Option c) (c) Since the sum of the probabilities is not equal to 1

Step-by-step explanation:

Given is a distribution of a random variable X as

x −3 1 5  

P(X=x) 1/2 5/8 3/4

We find that x can take only 3 values as 3,1,5

Since these are countable, this is discrete variable.

Yes.  Reason no of values that x can take is countable

b) Each prob lies between 0 and 1.

Total prob = [tex]\frac{1`}{2} +\frac{5`}{8} +\frac{3`}{4} >1[/tex]

Answer is

(c) Since the sum of the probabilities is not equal to 1

MrRoyal

A discrete probability is such that only take integer values.

The distribution is not a discrete distribution, since the sum of the probabilities is not equal to 1.

First, we calculate the sum of all probabilities.

For a discrete probability,

[tex]\sum P(x) = 1[/tex]

So, we have:

[tex]\frac 12 + \frac 58 + \frac 34 = 1[/tex]

Express as decimals

[tex]0.50 + 0.625 + 0.75 = 1[/tex]

[tex]1.875 = 1[/tex]

The above equation is not true, because:

[tex]1.875 \ne 1[/tex]

This means that: the distribution is not a discrete distribution, since the sum of the probabilities is not equal to 1.

Hence, (c) is true

Read more about discrete probabilities at:

https://brainly.com/question/17145091

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