(a) Give the definition of memoryless for a random
variable X. (b) Show that if X is an exponential
random variable with parameter λ , then X is memoryless.
(c) The life of the brakes on a car is exponentially distributed
with mean 50,000 miles. What is that probability that a car gets at
least 70,000 miles from a set of brakes if it already has
50,000 miles?
Subject: Statistics
Please show complete work for the multiple-choice
questions below
1. If the mean and median are equal, you know
that the:
a. distribution is symmetrical
b. distribution is skewed
c. distribution is normal
d. mode is equal to the median
2. The mean, median and mode are all measures
of:
a. the midpoint of the distribution
b. the most common score
c. percentile ranks
d. variability
3. Which of the following characterizes the
mean?
a. The sum of...
Topic:Physics statistics
1 a)Give definition of absolute temperature through entropy.
Using microcanonical formalism,show that for two systems in a state
of thermal equilibrium with each other, the equality of
temperatures follows from the fact that entropy is an extensive
quantity.
b)Explain if the absolute temperature can be negative or not. If
so, in what physical systems and why does this phenomenon
happen?
Show complete solution
1. Show that the lines ?/1 = y+3/ 2 = z+1/3 and x-3/2 = y/1 =
z-1/-1 intersect by finding their point of intersection. Find the
equation of the plane determined by these lines. Find parametric
equations for the line that is perpendicular to the two lines and
passes through their point of intersection.
1. Give a complete, all-encompassing definition of a gene.
Discuss each part of your definition. Is the definition of the gene
as determined through complementation, recombination, and mutation
for prokaryotes directly applicable to eukaryotes or must some
additional considerations be taken into account? Explain.
(a) Give a definition of a closed set.
(b) Show, directly from the definition, that a union of finitely
many closed sets is closed.
(c) Give an example of a countable collection of closed
intervals In such that ∪ n=1 to ∞ In is open (make sure
to prove it).
1. Use the ε-δ definition of continuity to prove that (a) f(x) =
x 2 is continuous at every x0. (b) f(x) = 1/x is continuous at
every x0 not equal to 0.
3. Let f(x) = ( x, x ∈ Q 0, x /∈ Q (a) Prove that f is
discontinuous at every x0 not equal to 0. (b) Is f continuous at x0
= 0 ? Give an answer and then prove it.
4. Let f and g...
Definition 1 (Topological space). Let X be a set. A collection O
of subsets of X is called a topology on the set X if the following
properties are satisfied:
(1) emptyset ∈ O and X ∈ O.
(2) For all A,B ∈ O, we have A∩B ∈ O (stability under
intersection).
(3) For all index sets I, and for all collections {Ui}i∈I of
elements of O (i.e., Ui ∈ O for all i ∈ I), we have U i∈I...
statistics students believe that the average score on
the first statistics test is 65. A statistics instructor thinks the
average score is higher than 65. he samples ten statistics students
and obtains the scores 65;65;70;67;66;63;63;68;72;7. he performs a
hypothesis test using a 5% level of significance. the data are from
a normal distribution.
A) use these data to compare a 95% confidence interval
for u.
B) is there enough evidence to reject the claim?
4. it has been reported that...