Virtual Labs

2. An experiment consists of flipping a coin until the first 'Heads' appears. Let the random variable X represent the number of flips required. Which distribution's PMF should be used to model X?

a: Binomial Explanation

Explanation

b: Poisson Explanation

Explanation

c: Bernoulli Explanation

Explanation

d: Geometric Explanation

Explanation

3. A discrete random variable X has a range of

\{1, 2, 3\}

and a PMF defined as

p_X(k) = c \cdot k^2

. What is the value of the constant

c

that makes this a valid PMF?

a: 1 Explanation

Explanation

b: 1/6 Explanation

Explanation

c: 1/14 Explanation

Explanation

d: 1/9 Explanation

Explanation

4. A continuous random variable X is uniformly distributed over the interval [0, 10]. Its PDF is

f_X(x) = 1/10

for

0 \leq x \leq 10

and 0 otherwise. What is the value of the CDF at

x=4

, i.e., what is

F_X(4)

a: 1/10 Explanation

Explanation

b: 4/10 Explanation

Explanation

c: 1 Explanation

Explanation

d: Cannot be determined Explanation

Explanation

5. Which statement is true for any continuous random variable X with PDF

f_X(x)

P(X=x) > 0

for some x. Explanation

Explanation

f_X(x)

represents the probability that the variable takes the value x. Explanation

Explanation

P(a < X < b) = P(a \leq X \leq b)

Explanation

d: The PDF

f_X(x)

must always be less than or equal to 1. Explanation

Explanation

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