If a random variable X is multiplied by a constant 'c', how does it affect its expected value?
E(cX) = E(X) / c
E(cX) = E(X) + c
E(cX) = E(X)
E(cX) = c * E(X)
What does the expected value (mean) of a random variable represent?
The average of all possible values, weighted by their probabilities.
The spread or dispersion of the variable's values.
The most frequent value the variable takes on.
The probability of the variable taking on a specific value.
If a random variable X represents the number of tails in two coin flips, what is P(X = 1) using its Probability Mass Function (PMF)?
1.00
0.25
0.75
0.50
What is the probability that a randomly selected person was born on a Tuesday, assuming births are equally likely on any day of the week?
1/52
1/365
1/12
1/7
How many different ways can you arrange the letters in the word "DATA"?
16
12
24
4
A bag contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball, then another red ball without replacement?
25/64
9/64
5/8
5/14
A website experiences an average of 5 user registrations per hour. What distribution best models the number of registrations in a given hour?
Geometric Distribution
Uniform Distribution
Poisson Distribution
Binomial Distribution
Which of the following is NOT a valid probability value?
1.25
1
0
You are playing a game where you roll a die until you get a 6. What is the probability that you will roll the die exactly 4 times before winning?
(1/6)^3 * (5/6)
(1/6)^4
(5/6)^3 * (1/6)
(5/6)^4 * (1/6)
A fair coin is flipped 5 times. What is the probability of getting exactly 3 heads?
1/8
1/2
5/16
3/16