The number of siblings of a class of students has the following probability dist
ID: 3230189 • Letter: T
Question
The number of siblings of a class of students has the following probability distribution. Suppose a student is picked at random from the class. Let X denote the number of siblings student. Then, X has the above distribution. (a) Confirm that this is in fact a probability distribution by stating all requirements which are met. (b) What is the chance that the student picked at random has at least one sibling? You may use the following table to help complete the calculations for parts c and d. Reminder: Don't forget to show correct symbol for both parts. (c) Find the mean (or expected value) for the number of siblings for a randomly selected student in this class. (d) Find the variance and standard deviation for the random variable X representing number of siblings.Explanation / Answer
Answer:
a).
x
0
1
2
3
4
5
Total
p(x)
0.2373
0.3955
0.2637
0.0879
0.0146
0.001
1
Each p(x) is between 0 and 1. p(x) =1.
Therefore this is a probability distribution.
b).P( atleast on sibling) = P( x1) =0.3955+0.2637+0.0879+0.0146+0.001
=0.7627
c).
x
0
1
2
3
4
5
Total
p(x)
0.2373
0.3955
0.2637
0.0879
0.0146
0.001
1
x*p(x)
0
0.3955
0.5274
0.2637
0.0584
0.005
1.25
x^2p(x)
0
0.3955
1.0548
0.7911
0.2336
0.025
2.5
Mean =xp(x) =1.25
d).
variance = x^2p(x)-mean^2 =2.5-1.25^2 = 0.9375
standard deviation = sqrt(0.9375) =0.968246
x
0
1
2
3
4
5
Total
p(x)
0.2373
0.3955
0.2637
0.0879
0.0146
0.001
1