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Ne4ueva [31]
3 years ago
15

Suppose N has a geometric distribution with parameter p. Derive a closed-form expression for E(N | N <= k), k = 1,2,... Check

via simulation for p = 0.2, k = 3.
Mathematics
1 answer:
vfiekz [6]3 years ago
3 0

Answer:

P(X= k) = (1-p)^k-1.p

Step-by-step explanation:

Given that the number of trials is

N < = k, the geometric distribution gives the probability that there are k-1 trials that result in failure(F) before the success(S) at the kth trials.

Given p = success,

1 - p = failure

Hence the distribution is described as: Pr ( FFFF.....FS)

Pr(X= k) = (1-p)(1-p)(1-p)....(1-p)p

Pr((X=k) = (1 - p)^ (k-1) .p

Since N<=k

Pr (X =k) = p(1-p)^k-1, k= 1,2,...k

0, elsewhere

If the probability is defined for Y, the number of failure before a success

Pr (Y= k) = p(1-p)^y......k= 0,1,2,3

0, elsewhere.

Given p= 0.2, k= 3,

P(X= 3) =( 0.2) × (1 - 0.2)²

P(X=3) = 0.128

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Ken normally leaves work at 5:00 pm, but he is leaving 20 minutes late today. He decides to make up time by taking the toll road
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Answer:

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Step-by-step explanation:

As stated in the question that x represents the number of minutes his <em>normal</em> commute takes. Here the keyword is normal; in the <em>normal</em> commute, Ken takes side streets instead of the toll road.

However, in this scenario, we have to come up with the equation that takes Ken's commute via <em>toll road</em>.

Ken can travel 3 times faster by taking the toll road (Given), which can be represented in the mathematical terms in terms of x as follows:

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<em>Without considering Ken getting late, </em>the equation would become the following:

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<em>As Ken is leaving late</em>, we have to incorporate that time as well by <em>adding</em> it in the aforementioned equation (A).

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