Probability and Statistics Annotated Bibilography 2022

Running head: PROBABILITY AND STATISTICS
Probability and Statistics
Name of the student:
Name of the University:
Author note:

PROBABILITY AND STATISTICS
1
Table of Contents
Answer to the question 1............................................................................................................2
Answer to the question 2............................................................................................................3
Answer to the question 3............................................................................................................3
Answer to the question 4............................................................................................................4
Answer to the question 5............................................................................................................5
Answer to the question 6............................................................................................................5
Answer to the question 7............................................................................................................5
Answer to the question 8............................................................................................................5
Answer to the question 9............................................................................................................6
Answer to the question 10..........................................................................................................6
Answer to the question 12..........................................................................................................7
Answer to the question 13..........................................................................................................7
Answer to the question 14..........................................................................................................8
Answer to the question 15..........................................................................................................8
Bibliography...............................................................................................................................9

PROBABILITY AND STATISTICS
2
Answer to the question 1
Given
fX, Y (x, y) = c 0≤ x ≤ 5
0≤ y ≤ 9
P (X≤ d) where d=2
Now
∫∫f ( x , y ) dx dy = 1
Or ∫
0
5
∫
0
9
c dx dy = 1
Or c (5-0) (9-0) = 1
Or c= 1/45
f X (x)= ∫
y
❑
c dy
=∫
0
9
1/ 45 dy
= 1/45 (9-0)
= 1/5
P(X≤ 2) = ∫
0
2
1/5 dx
= 1/5 (2-0)
= 2/5
= 0.4

PROBABILITY AND STATISTICS
3
Answer to the question 2
Y= aX2+b
a=1 and b= 2
E (X) =0 and V(X) =1
E (Y) = E (aX2+b)
= a E(X2) +b (expectations of constant is constant)
Now
V(X) = E(X2) – ((E(X))2
Or 1 = E(X2) – 0
E(X2) = 1
Now
E (Y) = 1* 1+2
=1+2
= 3
Answer to the question 3
Getting head = 1
Not getting head= 0
P= 0.5
Let X denote the total number of flip