How do I calculated the expected value of the sum of the greatest (or least) k of n independent uniformly...
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This question stemmed from asking myself how to calculate the expected value of the greater or lower of two dice rolls (k=1, n=2) but have phrased it more broadly for the sake of answering a larger question. Simple iterative code gives accurate approximations but I'm sure there's a way to determine a discrete answer that I don't know.
I don't need an exact answer, even guidance on the realm of probability to research would be great. Thanks!
probability statistics
asked Nov 24 '18 at 11:15
NaT3zNaT3z
203
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add a comment |
$begingroup$
This question stemmed from asking myself how to calculate the expected value of the greater or lower of two dice rolls (k=1, n=2) but have phrased it more broadly for the sake of answering a larger question. Simple iterative code gives accurate approximations but I'm sure there's a way to determine a discrete answer that I don't know.
I don't need an exact answer, even guidance on the realm of probability to research would be great. Thanks!
probability statistics
asked Nov 24 '18 at 11:15
NaT3zNaT3z
203
$endgroup$
add a comment |
$begingroup$
This question stemmed from asking myself how to calculate the expected value of the greater or lower of two dice rolls (k=1, n=2) but have phrased it more broadly for the sake of answering a larger question. Simple iterative code gives accurate approximations but I'm sure there's a way to determine a discrete answer that I don't know.
I don't need an exact answer, even guidance on the realm of probability to research would be great. Thanks!
probability statistics
asked Nov 24 '18 at 11:15
NaT3zNaT3z
203
$endgroup$
This question stemmed from asking myself how to calculate the expected value of the greater or lower of two dice rolls (k=1, n=2) but have phrased it more broadly for the sake of answering a larger question. Simple iterative code gives accurate approximations but I'm sure there's a way to determine a discrete answer that I don't know.
I don't need an exact answer, even guidance on the realm of probability to research would be great. Thanks!
probability statistics
probability statistics
asked Nov 24 '18 at 11:15
NaT3zNaT3z
203
asked Nov 24 '18 at 11:15
NaT3zNaT3z
203
asked Nov 24 '18 at 11:15
NaT3zNaT3z
203
asked Nov 24 '18 at 11:15
NaT3zNaT3z
203
asked Nov 24 '18 at 11:15
NaT3zNaT3z
203
203
add a comment |
add a comment |
1 Answer
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$begingroup$
Given independent real-valued random variables $X_1,dots,X_n$, you can compute the distribution of their maximum:
$$
P(max_{i=1,dots,n}X_i leq x) = Pleft(bigcap_{i=1}^n{{X_i leq x}}right) = prod_{i=1}^nP(X_i leq x)
$$
and then calculate the expected value.
answered Nov 24 '18 at 12:54
Tki DenebTki Deneb
29210
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add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
Given independent real-valued random variables $X_1,dots,X_n$, you can compute the distribution of their maximum:
$$
P(max_{i=1,dots,n}X_i leq x) = Pleft(bigcap_{i=1}^n{{X_i leq x}}right) = prod_{i=1}^nP(X_i leq x)
$$
and then calculate the expected value.
answered Nov 24 '18 at 12:54
Tki DenebTki Deneb
29210
$endgroup$
add a comment |
$begingroup$
Given independent real-valued random variables $X_1,dots,X_n$, you can compute the distribution of their maximum:
$$
P(max_{i=1,dots,n}X_i leq x) = Pleft(bigcap_{i=1}^n{{X_i leq x}}right) = prod_{i=1}^nP(X_i leq x)
$$
and then calculate the expected value.
answered Nov 24 '18 at 12:54
Tki DenebTki Deneb
29210
$endgroup$
add a comment |
$begingroup$
Given independent real-valued random variables $X_1,dots,X_n$, you can compute the distribution of their maximum:
$$
P(max_{i=1,dots,n}X_i leq x) = Pleft(bigcap_{i=1}^n{{X_i leq x}}right) = prod_{i=1}^nP(X_i leq x)
$$
and then calculate the expected value.
answered Nov 24 '18 at 12:54
Tki DenebTki Deneb
29210
$endgroup$
Given independent real-valued random variables $X_1,dots,X_n$, you can compute the distribution of their maximum:
$$
P(max_{i=1,dots,n}X_i leq x) = Pleft(bigcap_{i=1}^n{{X_i leq x}}right) = prod_{i=1}^nP(X_i leq x)
$$
and then calculate the expected value.
answered Nov 24 '18 at 12:54
Tki DenebTki Deneb
29210
answered Nov 24 '18 at 12:54
Tki DenebTki Deneb
29210
answered Nov 24 '18 at 12:54
Tki DenebTki Deneb
29210
answered Nov 24 '18 at 12:54
Tki DenebTki Deneb
29210
29210
add a comment |
add a comment |
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