Let Y_1 and Y_2 be discrete random variables with the joint probability given in the table...
Question:
Let {eq}Y_1 {/eq} and {eq}Y_2 {/eq} be discrete random variables with the joint probability given in the table below:
| Y_1 | ||||
| 0 | 1 | 2 | ||
| Y_2 | 0 | 0 | 0.20 | 0.15 |
| 1 | 0.20 | 0.20 | 0.10 | |
| 2 | 0.10 | 0.05 | 0 |
(a) Find the marginal density for {eq}Y {/eq}
(b) Are {eq}Y_1 {/eq} and {eq}Y_2 {/eq} independent? Show your reasoning.
(c) Find the conditional distribution of {eq}Y_1 {/eq} given {eq}Y_2 = 1 {/eq}
(d) Compute {eq}P(Y_1 = 1 | Y_2 \geq 1) {/eq}
Joint Probability distribution
The marginal distribution in Joint Probability distribution is calculated by integrating the variable joint PDF with respect to that particular variable under the given limit. The total of marginal distribution must also hold the property of a well-defined PDF.
Answer and Explanation: 1
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b
The probability when both Y1 and Y2 are 0 = 0
Probability when Y1 is 0 = 0.3
Probability when Y2 is 0 = 0.35
The product of both...
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Joint Probability | Definition, Formula & Calculation
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Chapter 12 / Lesson 14
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Learn what the joint probability of two independent events is. Understand how to calculate joint probability through using the joint probability formula.
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