Expert answer:Need math help with statistics
Answer & Explanation:TA-ACTIVITIES-1.pdfThis is my intro stats class and this one is a reminder of previous calculus class that either I forgot or I didn’t take.Hopefully you can also teach me what theory is it and where can I study more. Clear explanation is greatly appreciated :))Thank you !
ta_activities_1.pdf
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Stat 100 -Intro Probability
TA Session
J. Sanchez
UCLA Department of Statistics
Problem 1. What is the value of 5!? Show work.
Problem 2. What is the value of
7
Problem 3. What is the value of
4
? Show work.
20
3,10,7
? Show work and write this as a product of binomial coefficients.
Problem 4. Let f (x) = 0.75(1 − x2 ),
R1
(a) Find −1 x f (x)dx
(b) Find the value of c such that
(c) Find the function
x
−1
R
Rc
−1
−1 ≤ x ≤ 1. Solve the following, showing work.
f (x)dx = 0.5
f (t)dt in terms of x.
(d) Find the area under f (x) between −0.5 and 0.1
Problem 5. Consider the following definition:
Γ(α) =
Z
∞
e−y yα−1 dy
0
Solve the integral to show that
Γ(α) = (α − 1)Γ(α − 1)
You will need integration by parts.
Some of the math we need in Stat 100A
1
Stat 100 -Intro Probability
TA Session
J. Sanchez
UCLA Department of Statistics
Problem 6. Let f (x, y) = 6y,
Problem 7. What is
kn
n=0 n!
P∞
0 ≤ y ≤ x ≤ 1. Show that the volume under f (x, y) is 1.
equal to?
Problem 8. An auto insurance company has 10000 policy holders. Each policyholder is classified as
(1) young or old;
(2) male or female;
(3) married or single
Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. The policyholders can also be classified as 1320 young males, 3010 married males, and 1400 young married persons. Finally, 600 of the policyholders
are young married males. How many of the policyholders are young, female, and single? Draw Venn diagrams for the
events: Young (Y), Male (M) and married (m) and use them to illustrate your answer.
Problem 9. Find (i) the simplest symbolic expression for the following events and (ii) illustrate the left hand side
event with Venn Diagrams:
(a) (E ∪ F)(E ∪ F c ) =
(b) (E ∪ F)(E c ∪ F)(E ∪ F c ) =
(c) (E ∪ F)(F ∪ G) =
Some of the math we need in Stat 100A
2
…
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