Expected Value and Probability Concepts

The video tutorial explains how to analyze a discrete probability distribution for a random variable X. It covers finding the value of M by ensuring the sum of probabilities equals 1, and calculating the expected value or mean of X using given probabilities. The tutorial provides step-by-step calculations and explanations to help understand these concepts.

What does the first row in the probability distribution table represent?

• The expected value of the distribution

• The sum of all probabilities

• The values the random variable can assume

• The probabilities of each outcome

What must the sum of all probabilities in a probability distribution equal?

• 0.5

• 2

• 1

• 0

How is the value of M determined in the equation 0.4 + M + 3M = 1?

• By guessing

• By solving the equation

• By using a calculator

• By trial and error

What is the probability of the outcome when X equals 4?

• 0.4

• 0.45

• 0.6

• 0.15

If M is 0.15, what is the probability of the outcome when X equals 6?

• 0.45

• 0.3

• 0.15

• 0.6

What is the expected value of a random variable?

• The most frequent value

• The highest possible value

• The average or mean value

• The sum of all possible values

Which formula is used to calculate the expected value of a random variable?

• Difference of values

• Summation of each value times its probability

• Sum of values

• Sum of probabilities

What is the expected value of X if the probabilities are 0.4, 0.15, and 0.45 for values 2, 4, and 6 respectively?

• 3.5

• 4.1

• 4.5

• 5.0

How do you calculate the contribution of each value to the expected value?

• Multiply the value by its probability

• Divide the value by its probability

• Add the value to its probability

• Subtract the probability from the value

What is the final step in calculating the expected value?

• Multiplying all contributions

• Adding all contributions

• Subtracting all contributions

• Dividing all contributions