Inside of a jar are four balls that are labeled 1, 2, 3, and 4. You randomly choose three balls from the jar (w/ replacement). Let X = smallest of the three numbers on the balls selected (i) What is the pmf for X? (ii) What is the CDF for X? (iii) What is P(X<3)?
Inside of a jar are four balls that are labeled 1, 2, 3, and 4. You randomly choose three balls from the jar (w/ replacement). Let X = smallest of the three numbers on the balls selected
(i) What is the pmf for X?
(ii) What is the CDF for X?
(iii) What is P(X<3)?
Basic Probability: You should be familiar with fundamental concepts of probability, such as sample spaces, events, and probability calculations. This includes understanding concepts like independence, conditional probability, and random variables.
Random Variables: Understanding what a random variable is and how to work with it is essential. In this problem, X is a random variable representing the smallest number on the balls selected.
Probability Mass Function (PMF): You should know what a PMF is and how to calculate probabilities for discrete random variables. In this problem, you need to determine the probabilities for different values of X.
Cumulative Distribution Function (CDF): Understanding the CDF for a random variable and how it relates to the PMF is important. The CDF represents the cumulative probability up to a certain point.
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