In Problems 15–22 , use the given information to sketch the graph of f. Assume that f is continuous on its domain and that all intercepts are included in the table of values. 18. Domain: All real x , except x = 1; lim x → 1 − f ( x ) = ∞ ; lim x → 1 + f ( x ) = ∞ ; lim x → ∞ f ( x ) = − 2 x −4 −2 0 2 f ( x ) 0 −2 0 0
In Problems 15–22 , use the given information to sketch the graph of f. Assume that f is continuous on its domain and that all intercepts are included in the table of values. 18. Domain: All real x , except x = 1; lim x → 1 − f ( x ) = ∞ ; lim x → 1 + f ( x ) = ∞ ; lim x → ∞ f ( x ) = − 2 x −4 −2 0 2 f ( x ) 0 −2 0 0
Solution Summary: The author illustrates the graph of the function f(x) from the given information.
In Problems 15–22, use the given information to sketch the graph of f. Assume that f is continuous on its domain and that all intercepts are included in the table of values.
18. Domain: All real x, except x = 1;
lim
x
→
1
−
f
(
x
)
=
∞
;
lim
x
→
1
+
f
(
x
)
=
∞
;
lim
x
→
∞
f
(
x
)
=
−
2
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.
iid
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 4 Solutions
Calculus for Business Economics Life Sciences and Social Sciences Plus NEW
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