Probability Random variables help

In summary, the conversation is about finding the probability of Y=5 given a specific probability distribution function and the values of X1 and X2. The solution involves breaking down the probability into two separate events and using the fact that X1 and X2 are independent.
  • #1
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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 [Broken]

Thanks.
 
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  • #2
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
 
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  • #3
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.
 

1. What is the difference between probability and random variables?

Probability is the likelihood of a certain event occurring, while random variables are variables that can take on different values depending on the outcome of an experiment or event.

2. How do you calculate the probability of a random variable?

To calculate the probability of a random variable, you need to first determine the possible outcomes and their associated probabilities. Then, you can use the formula P(X = x) = probability of x to calculate the probability of a specific value of the random variable.

3. What is the purpose of using random variables in probability?

Random variables allow us to mathematically model and analyze real-world situations that involve uncertainty. This helps us make predictions and decisions based on the likelihood of different outcomes.

4. Can a random variable have a negative probability?

No, a probability cannot be negative. However, a random variable can take on negative values, but the probability of those values must be greater than or equal to 0.

5. How do you interpret the expected value of a random variable?

The expected value of a random variable represents the average value that is expected to be obtained in repeated trials of an experiment. It is calculated by multiplying each possible value of the random variable by its probability and summing the results.

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