Solve Probability Questions: Find E[X], E[2^X], & More

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SUMMARY

The discussion focuses on solving probability questions involving random variables and their properties. The first problem requires finding the constant k for the probability mass function (PMF) of a discrete random variable X, followed by calculating the expected value E[X] and variance var(X), as well as E[2^X]. The second problem involves a joint PMF of random variables X and Y, where participants are tasked with finding the normalization constant c, marginal PMFs, and expected values. The discussion emphasizes the importance of showing attempted solutions for homework-related queries.

PREREQUISITES
  • Understanding of discrete random variables and probability mass functions (PMFs)
  • Knowledge of expected value and variance calculations
  • Familiarity with joint probability distributions
  • Ability to manipulate and solve equations involving random variables
NEXT STEPS
  • Learn how to derive normalization constants for probability mass functions
  • Study the properties of expected values for functions of random variables
  • Explore variance calculations for linear combinations of random variables
  • Investigate joint distributions and their marginal distributions in depth
USEFUL FOR

Students studying probability theory, educators teaching statistics, and anyone involved in solving complex probability problems in academic settings.

sinyoungoh
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probability question please help!

i need full working out process...
thanks for helping me :)
1. Let X be a random variable with PMF
x 0 1 2 3 4
p(x) 5k 4k 3k 2k k

(a) Find k.
(b) Find E[X] and var(X).
(c) Find E[2^X].

2. The joint PMF of X and Y is pX;Y (x; y) = c(x2 + y2), x; y = 1; 2; 3. Find
(a) c and the marginal PMFs of X and Y
(b) E[X]
(c) The PMF of 3X - 2Y
(d) E[3X - 2Y ] in two ways.
 
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This looks like homework, and thus belongs in a homework forum (read the stickies!)

Show us what you've attempted so far.
 

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