Let S be a sample space and E and F be events associated with. Suppose that Pr ( E ) = .4 , Pr ( F | E ) = .25 , and Pr ( F ) = .3 . Calculate a. Pr ( E ∩ F ) b. Pr ( E ∪ F ) c. Pr ( E | F ) d. Pr ( E ′ ∩ F ) .
Let S be a sample space and E and F be events associated with. Suppose that Pr ( E ) = .4 , Pr ( F | E ) = .25 , and Pr ( F ) = .3 . Calculate a. Pr ( E ∩ F ) b. Pr ( E ∪ F ) c. Pr ( E | F ) d. Pr ( E ′ ∩ F ) .
Solution Summary: The author calculates the value of Pr(Ecap F) if the sample space is S and the events are E and F.
Let S be a sample space and E and F be events associated with. Suppose that
Pr
(
E
)
=
.4
,
Pr
(
F
|
E
)
=
.25
,
and
Pr
(
F
)
=
.3
. Calculate
a.
Pr
(
E
∩
F
)
b.
Pr
(
E
∪
F
)
c.
Pr
(
E
|
F
)
d.
Pr
(
E
′
∩
F
)
.
Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
Is it possible to show me how to come up with an exponential equation by showing all the steps work and including at least one mistake that me as a person can make. Like a calculation mistake and high light what the mistake is. Thanks so much.
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1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a
random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution
depend on the mean and variance of the underlying random variables (i.e., the population
mean and variance). The approximation can be written to emphasize this, using the expec-
tation and variance of one of the random variables in the sample instead of the parameters
μ, 02:
YNEY,
· (1
(EY,, varyi
n
For the following population distributions f, write the approximate distribution of the sample
mean.
(a) Exponential with rate ẞ: f(y) = ß exp{−ßy}
1
(b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ }
г(
(c) Poisson with rate λ: P(Y = y) = exp(-\}
>
y!
y²
2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the
CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and
the standard normal CDF Fz(·).
Chapter 6 Solutions
Finite Mathematics & Its Applications (12th Edition)
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