1. Let X be a continuous random variable with a pdf function f(x) that is symmetric around 0 (i.e. f(x) = f(-x) for every x). Compute the probability that X > 0

• A: 1/2
• B: Cannot be known; depends on the pdf function f(x)
• C: 1/4
• D: 1

2) Let X have a normal distribution N (mu = 10, sigma squared = 36), and f(x) denotes the pdf function of X compute the integral from -infinity to infinity x f(x) dx.

A. 6

B. 10

C. 36

D. 1

3). Let X have a normal question N (mu = 10; sigma squared = 36), and f(x) denotes the pdf function of X compute the following integral from -infinity to infinity (x-10)f(x)dx

A. none

B. 0

C. 10

D. -10

4). Let X have a normal distribution N (mu = 10, sigma squared = 36), and f(x) denotes the pdf function of X compute the integral from negative infinity to infinity (x^2+5) f(x)dx

A. 41

B. 5

C. 0

D. 141

5). Let X be a continuous random variable with pdf function f(x). Answer to which probabilities the following integrals correspond to respectively. Write the answers in the format: P(X < a), P(X>b), or P(a < X < b)

• integral from -10 to 10 f(x) dx
• Integral from negative infinity to 5 f(x)dx