Probability Random variables help

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SUMMARY

The discussion focuses on solving a probability problem involving random variables X1 and X2, specifically finding the probability that their sum Y equals 5. The solution utilizes the independence of X1 and X2, applying the formula P(Y=5) = P(X1=2) * P(X2=3) + P(X1=3) * P(X2=2). Participants emphasized the importance of referencing the provided probability distribution function to obtain the necessary probabilities for the calculations.

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  • Understanding of random variables and their properties
  • Knowledge of probability distribution functions
  • Familiarity with the concept of independence in probability
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Homework Statement



Can anyone help me with question 5d on this paper, I just don't get it.

I have done 5a,5b and 5c.

How do I find the values for x1 and x2 ?

http://www.mathspapers.co.uk/Papers/edex/S1Jan03Q.pdf

Thanks.
 
Last edited by a moderator:
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Let Y= X1 + X2

then we want the probability that Y=5

P(Y=5) = P(X1=2 , X2=3) + P(X1=3 , X2=3)

and since X1 and X2 are independent

P(Y=5) = P(X1=2)*P(X2=3) + P(X1=3)*P(X2=2)

and then just find the probabilites from the given probability distribution function
 
Last edited:
Random Variable said:
Let Y= X1 + X2

then we want the probability that Y=5

P(Y=5) = P(X1=2 , X2=3) + P(X1=3 , X2=3)

and since X1 and X2 are independent

P(Y=5) = P(X1=2)*P(X2=3) + P(X1=3)*P(X2=2)

and then just find the probabilites from the given probability distribution function

Oh I see that makes so much sense now, Thanks.
 

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