11.5 - Examples
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Practice Questions
Test your understanding with targeted questions
What is the MGF of a discrete random variable taking values 0 and 1 with equal probability?
💡 Hint: Use the definition of MGF, E[e^(tX)].
Calculate the mean of a discrete random variable that takes on values 1 and 3 with probabilities 1/4 and 3/4 respectively.
💡 Hint: Use the formula E[X] = Σ(x * P(X=x)).
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the MGF of a discrete random variable with possible values 0 and 1 each with probability 1/2?
💡 Hint: Recall the formula for the MGF.
True or False: The mean of a normally distributed random variable is always zero.
💡 Hint: Consider the definition of a normal distribution.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
💡 Hint: Use the definition of MGF and the formulas for mean and variance.
Assume Y ~ N(μ, σ²). Prove that the mean can be derived from the MGF.
💡 Hint: Differentiate the MGF and evaluate at t=0.
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Reference links
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