Calculating Expected Value of a Random Variable: Solving for E[X]

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SUMMARY

The discussion focuses on calculating the expected value E[X] of a random variable X, which can take values 0, 1, and 2. The probability mass function is defined as P{X = i} = cP{X = i - 1} for i = 1, 2, where c is a constant. Participants suggest expressing P(X=i) as p_i to derive p_2 and p_3 in terms of c and p_0. The solution involves setting up an equation based on the normalization condition that the sum of probabilities equals 1, ultimately leading to a formula for E[X] that incorporates the constant c.

PREREQUISITES
  • Understanding of probability mass functions
  • Familiarity with expected value calculations
  • Knowledge of normalization conditions in probability
  • Basic algebra for solving equations
NEXT STEPS
  • Study the derivation of expected value for discrete random variables
  • Learn about probability mass functions and their properties
  • Explore normalization conditions in probability theory
  • Practice solving equations involving constants in probability distributions
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Students studying probability theory, mathematicians interested in random variables, and educators teaching concepts of expected value and probability distributions.

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Homework Statement



Suppose that X takes on one of the values 0, 1, and 2. If for some constant c, P{X = i} = cP{X = i - 1}, i = 1, 2. Find E [X]


Homework Equations





The Attempt at a Solution



I'm not sure how to start this. A push in the right direction would be awesome.

Thanks!
 
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changeofplans said:

Homework Statement



Suppose that X takes on one of the values 0, 1, and 2. If for some constant c, P{X = i} = cP{X = i - 1}, i = 1, 2. Find E [X]


Homework Equations





The Attempt at a Solution



I'm not sure how to start this. A push in the right direction would be awesome.

Thanks!

I will call ##P(X=i) = p_i## to save typing. You can get ##p_2## and ##p_3## in terms of ##c## and ##p_0##. You know the ##p_i## add to 1. That will give you an equation with ##c## and ##p_0##. Crank out the formula for ##E(X)## and you should be able to get an answer that depends on ##c##.
 

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