## Recent **Performance Management** Questions & Answers

###### Certain measurements are assumed to be normally distributed with
25 as the mean 25 and 0.5 as the standard deviation. What is the probability
that a m...

##### Certain measurements are assumed to be normally distributed with
25 as the mean 25 and 0.5 as the standard deviation. What is the probability
that a measurement lies between 23 and 27?...

###### Using the Stirling approximation and a procedure similar to the one
used for binomial distribution in the text, show that in the limit of large
n and ...

##### Using the Stirling approximation and a procedure similar to the one
used for binomial distribution in the text, show that in the limit of large
n and ?, the Poisson distribution of Equation (32.43) becomes the normal
distribution....

###### Using partial fractions write the integrand of Example 32.4.3 as
1
(v2 + 1)[(u ? v)2 + 1]
= av + b
v2 + 1
+ cv + d
(u ? v)2 + 1.
Now write the right-h...

##### Using partial fractions write the integrand of Example 32.4.3 as
1
(v2 + 1)[(u ? v)2 + 1]
= av + b
v2 + 1
+ cv + d
(u ? v)2 + 1.
Now write the right-hand side as a single fraction with the same denominator
as the left-hand side. Set the coefficients of the powers of v in the numerator
equal to zero,...

###### Let c be a positive constant and
f(x, y) =
0cx(x + y) if0< x, 0 < y < 1;
0 otherwise.
Let u = x + y. Show that the density h(u) for the variable u is
...

##### Let c be a positive constant and
f(x, y) =
0cx(x + y) if0< x, 0 < y < 1;
0 otherwise.
Let u = x + y. Show that the density h(u) for the variable u is
h(u) =
0cu3/2 if0< u < 1;
cu(u ? 1
2) if u > 1.
Show that this can be written as
h(u) = cu.?(u)?(1 ? u)u2/2 + ?(u ? 1)(u ? 1
2 )/....

###### Show that
# t
0
# t1
0
...

##### Show that
# t
0
# t1
0
...

###### Consider the nonnegative function
x(t) = [t(x? ? X? ) + (x? ? X? )]2 .
(a) Show that
x(t) = t2?2(X?) + 2tcov(X?,X?) + ?2(X?),
which is a parabola i...

##### Consider the nonnegative function
x(t) = [t(x? ? X? ) + (x? ? X? )]2 .
(a) Show that
x(t) = t2?2(X?) + 2tcov(X?,X?) + ?2(X?),
which is a parabola in the tx-plane.
(b) If the parabola is to be nonnegative, it should have at most one real root.
Show that for this to happen, the following inequality...

###### The uniform probability density function over (a, b) is
f(x) =
01/(b ? a) if a < x < b;
0 otherwise.
What is the expectation value X for this distri...

##### The uniform probability density function over (a, b) is
f(x) =
01/(b ? a) if a < x < b;
0 otherwise.
What is the expectation value X for this distribution?...

###### Suppose that ? is a function of x? alone and x? is independent of
the rest of the variables of f(x), the density function for a multidimensional
proba...

##### Suppose that ? is a function of x? alone and x? is independent of
the rest of the variables of f(x), the density function for a multidimensional
probability space. Show that
?(X?) = # #
?
?(x?)f(x) dmx = #
?
??
?(x?)g(x?) dx?....

###### One of the first excited states of the H-atom has the wave function
?(r, ?, ?) = Are
?r/2a0 cos ?. (a) Find A so that ?(r, ?, ?) is normalized to 1.
(...

##### One of the first excited states of the H-atom has the wave function
?(r, ?, ?) = Are
?r/2a0 cos ?. (a) Find A so that ?(r, ?, ?) is normalized to 1.
(b) Evaluate X , Y , and Z . Are they all zero? Do you expect them to
be?
(c) What is the expectation value of the distance of the electron from th...

###### The number of ? particles emitted from a sample of a radioactive
atom is counted every minute for 50 hours. The total count is 1500.
(a) What is ? for...

##### The number of ? particles emitted from a sample of a radioactive
atom is counted every minute for 50 hours. The total count is 1500.
(a) What is ? for this Poisson distribution?
(b) What is the probability that in the next 6 minutes three ? particles will
be emitted?
(b) What is the probability that...