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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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transcribe in digital format please
![Solution
Let x be the sundom variable with
део ср)
then we have to show that for my, `n, m>, o in
P(x>n+m | X > m ) =P ( X = n)
oo X~ geo(P) the pmf of x-
-
If
f(x) = P(x=) = 2 2-1 p
р
we have
for any positive integer. K
∞
P(X>K) = = P(X=~) = { 2²-1 |
41=1+1
x=k+1
-
P(X>K) = b[qk+qkt |___ ] = b₂k
J
P(xxn+m/ x7m)
2 = 1-p, x = 1, 2, 3, ___
)
P ( x 7₂n+mn x>,m)
P(x>m)
mm
= 2n+m
qm
हात
In, and m are any two positive inters then, we have
1-2
6+2=1
in tegers-
=
a
2n = P(x7n) using eqla).
= P ( X = n)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbaddd2dc-7ae1-44a5-8eff-7edb2838a5d7%2F06cdc1de-57cc-485e-85fe-2274e5870f38%2F3egqi7w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solution
Let x be the sundom variable with
део ср)
then we have to show that for my, `n, m>, o in
P(x>n+m | X > m ) =P ( X = n)
oo X~ geo(P) the pmf of x-
-
If
f(x) = P(x=) = 2 2-1 p
р
we have
for any positive integer. K
∞
P(X>K) = = P(X=~) = { 2²-1 |
41=1+1
x=k+1
-
P(X>K) = b[qk+qkt |___ ] = b₂k
J
P(xxn+m/ x7m)
2 = 1-p, x = 1, 2, 3, ___
)
P ( x 7₂n+mn x>,m)
P(x>m)
mm
= 2n+m
qm
हात
In, and m are any two positive inters then, we have
1-2
6+2=1
in tegers-
=
a
2n = P(x7n) using eqla).
= P ( X = n)
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