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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the MGF of a discrete random variable taking values 0 and 1 with equal probability?
π‘ Hint: Use the definition of MGF, E[e^(tX)].
Question 2
Easy
Calculate the mean of a discrete random variable that takes on values 1 and 3 with probabilities 1/4 and 3/4 respectively.
π‘ Hint: Use the formula E[X] = Ξ£(x * P(X=x)).
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the MGF of a discrete random variable with possible values 0 and 1 each with probability 1/2?
- (1 + e^t)/2
- (1 + e^(t/2))/2
- e^t
π‘ Hint: Recall the formula for the MGF.
Question 2
True or False: The mean of a normally distributed random variable is always zero.
- True
- False
π‘ Hint: Consider the definition of a normal distribution.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A discrete random variable X takes values 2, 3, and 5 with probabilities 0.3, 0.5, and 0.2 respectively. Calculate the MGF and derive the mean and variance.
π‘ Hint: Use the definition of MGF and the formulas for mean and variance.
Question 2
Assume Y ~ N(ΞΌ, ΟΒ²). Prove that the mean can be derived from the MGF.
π‘ Hint: Differentiate the MGF and evaluate at t=0.
Challenge and get performance evaluation