Respuesta :
Answer:
[tex]c = \displaystyle\frac{1}{15}[/tex]
Step-by-step explanation:
We are given the following information:
[tex]f(x) = cx, ~x =1,2,3,4,5\\~~~~~~~=0, \text{otherwise}[/tex]
Thus, we can write:
[tex]f(1) = c\\f(2) = 2c\\f(3) = 3c\\f(4) = 4c\\f(5) = 5c[/tex]
Now, by property of probability mass function, we get:
[tex]\displaystyle\sum f(x) = 1\\\\c+2c+3c+4c+5c = 1\\15c = 1\\\\c = \displaystyle\frac{1}{15}[/tex]
The sum of the probabilities of all outcomes must be one. Then the value of constant c is 1/15.
What is probability?
Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Given
The probability mass function f(x) = cx .
If x = 1, 2, 3, 4, 5, 0, otherwise.
Thus, we can write
[tex]\rm f(1) = c\\\\f(2) = 2c\\\\f(3) = 3c\\\\f(4) = 4c\\\\f(5) = 5c[/tex]
By the property of probability of the mass function, we get
[tex]\Sigma f(x) = 1[/tex]
Then
[tex]c +2c +3c +4c +5c = 1[/tex]
On simplifying, we have
[tex]\rm 15c = 1\\\\c \ \ \ = \dfrac{1}{15}[/tex]
Thus, the value of c is 1/15.
More about the probability link is given below.
https://brainly.com/question/795909
