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STAT 20: Introduction to Probability and Statistics

- Concept review
- Concept questions
- PS 10
- Break
- Lab 3 slides
- Lab 3

Let \(X\) be a random variable such that \[ X = \begin{cases} -1, & \text{ with probability } 1/3\\ 0, & \text{ with probability } 1/6\\ 1, & \text{ with probability } 4/15 \\ 2, & \text{ with probability } 7/30 \\ \end{cases} \]

- Draw the graph of the cdf of \(X\)

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- Compute the expected value and variance of \(X\)

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\(X\) is a random variable with the distribution shown below:

\[ X = \begin{cases} 3, \; \text{ with prob } 1/3\\ 4, \; \text{ with prob } 1/4\\ 5, \; \text{ with prob } 5/12 \end{cases} \]

Consider the box with tickets: \(\fbox{3}\, \fbox{3}\, \fbox{3} \,\fbox{4} \,\fbox{4} \,\fbox{4} \,\fbox{4} \,\fbox{5} \,\fbox{5}\, \fbox{5} \,\fbox{5} \,\fbox{5}\)

Suppose we draw once from this box and let \(Y\) be the value of the ticket drawn. Which random variable has a higher expectation?

The expected value of \(X\) is ____ the expected value of \(Y\).

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Prof. Stoyanov’s Zoom office hours are not too crowded this spring. She observes that number of Stat 20 students coming to her Thursday office hours have a Poisson(2) distribution. There is one Data 88 student from a previous semester who is *always* there (they want a letter of recommendation).

What is the expected value (EV) and variance (V) of the number of students in her Zoom office hours?

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Let \(X\) be a discrete uniform random variable on the set \(\{-1, 0, 1\}\).

If \(Y=X^2\), what is \(E(Y)\)?

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Let \(X\) be a discrete uniform random variable on the set \(\{-1, 0, 1\}\).

If \(W = \min(X, 0.5)\), what is \(E(W)\)?

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