Probability Function Homework: Solving Parts (d), (e) & (f)

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SUMMARY

The discussion focuses on solving parts (d), (e), and (f) of a probability function homework problem involving a discrete random variable X with a defined probability function. The constant k is determined to be 0.25, which is essential for normalizing the probability function. The user seeks assistance in calculating P(X1 + X2 = 5), the complete probability function for X1 + X2, and the probability P(1.3 < X1 + X2 < 3.2). The problem emphasizes the importance of understanding the properties of discrete random variables and their associated probability distributions.

PREREQUISITES
  • Understanding of discrete random variables
  • Knowledge of probability functions and normalization
  • Familiarity with expectation and variance calculations
  • Ability to work with independent random variables
NEXT STEPS
  • Study the derivation of probability functions for discrete random variables
  • Learn how to calculate the expectation E(X) and variance Var(X)
  • Explore the convolution of probability distributions for sums of independent variables
  • Investigate the properties of cumulative distribution functions (CDFs) for continuous intervals
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Students studying probability theory, particularly those preparing for exams in statistics or mathematics, and anyone needing to solve problems involving discrete random variables and their properties.

aurao2003
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Homework Statement


Hi
I am trying to solve the d, e and f parts of this problem

The discrete random variable X has probability function
where k is a positive constant.

P(X = x) ={k(2 – x), x = 0, 1, 2,
k(x – 2), x = 3,
0, otherwise,

(a) Show that k = 0.25.
(b) Find E(X) and show that E(X 2) = 2.5.
(c) Find Var(3X – 2).
Two independent observations X1 and X2 are made of X.
(d) Show that P(X1 + X2 = 5) = 0.
(e) Find the complete probability function for X1 + X2.
(f) Find P(1.3 < X1 + X2 < 3.2).

Not sure how to begin. Please help. The exam is tomorrow.



Homework Equations





The Attempt at a Solution

 
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For (a), what must be the answer if you sum P(X = x) over x = 0, 1, 2, 3?
 

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