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

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In summary, the conversation is about a probability question that requires finding the value of k and solving for expected value and variance. The conversation also involves finding the joint PMF and marginal PMFs of X and Y, as well as calculating E[X] and the PMF of 3X - 2Y. The individual requesting help is advised to post their attempted solution on a homework forum.
  • #1
sinyoungoh
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probabilty 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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  • #2


This looks like homework, and thus belongs in a homework forum (read the stickies!)

Show us what you've attempted so far.
 

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

1. What is the formula for calculating expected value (E[X])?

The formula for calculating expected value is E[X] = ∑xP(x), where x represents each possible outcome and P(x) represents the probability of that outcome occurring.

2. How do you find the expected value for a given probability distribution?

To find the expected value for a given probability distribution, you multiply each possible outcome by its corresponding probability and then add all of these products together. This will give you the expected value, or average, of the distribution.

3. What is the significance of E[2^X] in probability questions?

E[2^X] is the expected value of 2 to the power of X. It is often used in probability questions because it can represent a variety of real-world scenarios, such as doubling a bet or the number of bacteria in a sample after a certain amount of time.

4. How can expected value be used to make decisions in probabilistic scenarios?

Expected value can be used to make decisions in probabilistic scenarios by helping us determine the most likely outcome and the potential payoff or loss associated with that outcome. It can also be used to compare different options and choose the one with the highest expected value.

5. Can expected value be calculated for continuous probability distributions?

Yes, expected value can be calculated for both discrete and continuous probability distributions. For continuous distributions, the sum in the formula is replaced with an integral.

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