Download Review Questions for Midterm 1. What is a random variable? 2

Review Questions for Midterm
1. What is a random variable?
2. What is the relationship between a random variable and data or observations on a random
variable?
3. What is a pdf and what role does it play?
4. What conditions must be fulfilled for a function to be a pdf?
5. Write the formulas for the following discrete pdfs:
a. Bernoulli (p) b. Binomial(N, p)
c. Uniform (0,4)
d. Poisson (λ) e. Geometric (r)
6. Write the formulas for the following continuous pdfs:
a. Negative Exponential (λ)
b. Standard Normal
c. Uniform (0,4)
d. Normal (μ,σ2)
7. Suppose that X is a random variable with continuous pdf, f(s). Explain how you would find
the following probability P[1  X  3] .
8. Suppose f(1) = 1/2, f(2) = 1/16, and f(3) = 1/8 with f(s) = 0 elsewhere. Explain why that f(s) is
not a pdf.
9. Suppose that you flip a fair coin twice. Write down the pdf for this random event.
10. Probability and statistics involves consideration of both theoretical and empirical worlds.
Explain.
11. Suppose the you have a random variable X that is distributed as a negative exponential
with   4 . Find P [0.25  X  0.35] .
12. There is no such thing as P [ Hillary Clinton will be elected President ] . Explain this.
13. Suppose X is distributed as a standard normal random variable. Find approximately
P [1.25  X  1.65] .
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14. Suppose X is distributed as a normal random variable with   5 and   4 . Find
approximately P [4  X  8] .
15. What is the big difference between classical probability and modern probability?