SOLUTION: i would be glad if you could help check if my answers are correct Consider the following discrete probability distribution function for the variable X: x 10 12 14 16 18 f(

Question 762057: i would be glad if you could help check if my answers are correct
Consider the following discrete probability distribution function for the variable X:
x
10
12
14
16
18
f(x)
.02
.7
.05
.2
.03 P.s this is a table showing corresponding values of x and f(x)
a) Is this a proper probability mass function? How do you know?
b) What is the probability that any draw from this distribution, say X, is less than 16 [i.e. find P(X<16)]?
answers i arrived at but not sure about them yet;
Yes this is a proper probability mas function because 0 < f(x) ≤ 1 and the sum of all the f(x)values is 1

The formula for probability is as follows;
P (E) = The Number Of Ways Event can occur/The total number Of Possible Outcomes
The probability that P(X<16) = Number of X values less than 16/The total number of values
According to the table the number of values less than 16 is 3 (i.e. 10, 12, 14) and the total number of values is 5
Therefore The probability that P(X<16) = 3/5 =0.6

Found 2 solutions by stanbon, DrBeeee:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Consider the following discrete probability distribution function for the variable X:
x
10
12
14
16
18
--------------------
f(x)
.02
.7
.05
.2
.03
-------------------
P.s this is a table showing corresponding values of x and f(x)
a) Is this a proper probability mass function? How do you know?
Each probability is between -1 and +1
The sum of the probabilities = 1
==========================================
b) What is the probability that any draw from this distribution, say X, is less than 16 [i.e. find P(X<16)]?
---
Ans: 0.02+0.70+0.05 = 0.75
================================================
answers i arrived at but not sure about them yet;
Yes this is a proper probability mas function because 0 < f(x) ≤ 1 and the sum of all the f(x)values is 1
The formula for probability is as follows;
P (E) = The Number Of Ways Event can occur/The total number Of Possible Outcomes
The probability that P(X<16) = 0.02+0.70+0.05 = 0.75
===============
Cheers,
Stan H.
====================

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
THe first answer re proper distribution function is correct.
However your second answer assumes that 10, 12, and 14 are each equally likely (same probability). The correct answer is
(1) P(x<16) = 0.02 + 0.70 + 0.05 or
(2) P(x<16) = 0.77 or
(3) P(x<16) = 77%

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