Question

1. A coin is tossed 3 times. Let x be the random discrete variable representing the number of times tails comes up.

a) Create a sample space for the event;

b) Create a probability distribution table for the discrete variable x;

c) Calculate the expected value for x.

2. For the data below, representing a sample of times (in
minutes) students spend solving a certain Statistics problem, find
P_{35}, range, Q_{2} and IQR.

3.0, 3.2, 4.6, 5.2 3.2, 3.5

3. Canadian Blood Services is a not-for-profit organization that collects nearly one million units of blood per year. About 6% of people have O-negative blood. They are called universal donors because O-negative blood can be given to anyone, regardless of the recipient’s blood type. Suppose that 25 blood donors arrive at one of this organization’s donation centres.

a) Find the expected value and standard deviation

b) What is the probability that there are exactly three universal donors?

c) What is the probability that there are less than three universal donors?

d) What is the probability that there are at least 2 donors?

=> I need steps to solve this questions. Please writing clearly

Answer #1

Let X be the random variable representing the difference between
the number of headsand the number of tails obtained when a fair
coin is tossed 4 times.
a) What are the possible values of X?
b) Compute all the probability distribution of X?
c) Draw the cumulative distribution function F(x) of the random
variable X.

Suppose a coin is tossed three times and let X be a random
variable recording the number of times heads appears in each set of
three tosses. (i) Write down the range of X. (ii) Determine the
probability distribution of X. (iii) Determine the cumulative
probability distribution of X. (iv) Calculate the expectation and
variance of X.

1. A fair coin will be tossed 200,000 times. Let X denote the
number of Tails. (a) What is the expected value and the standard
deviation of X? (b) Consider a game in which you have to pay $5 in
order to earn $log10(X) when X > 0. Is this a fair game? If not,
your expected profit is positive or negative?

1) An irregular coin (? (?) = ?? (?)) is thrown 3 times. ?
discrete random variable; ? = "number of heads - number of tails"
is defined. Accordingly, ? is the discrete random variable
number of heads - number of posts
a) Find the probability distribution table.
b) Cumulative (Additive) probability distribution table; ?
(?)
c) Find ? (?≥1).

1. Let the random variable X represent the number of walks you
take a day. Also, assume that the number of walks you
take is uniformly distributed between 0 and 3; that is, you are
equally likely to take 0, 1, 2, or 3 walks a day.
a.What type of distribution is the random variable X?
b. What is the probability that on a randomly chosen day, you
walk exactly 0 walks?
c. What is the probability that on a...

A coin is tossed 5 times. Let the random variable ? be the
difference between the number of heads and the number of tails in
the 5 tosses of a coin. Assume ?[heads] = ?.
Find the range of ?, i.e., ??.
Let ? be the number of heads in the 5 tosses, what is the
relationship between ? and ?, i.e., express ? as a function of
??
Find the pmf of ?.
Find ?[?].
Find VAR[?].

A fair coin has been tossed four times. Let X be the number of
heads minus the number of tails (out of four tosses). Find the
probability mass function of X. Sketch the graph of the probability
mass function and the distribution function, Find E[X] and
Var(X).

2.
The incomplete
probability distribution table at the right is of the discrete
random variable x representing the number of times people
donate blood in 1 year. Answer the following:
x
P(X=x)
(a)
Determine the
value that is missing in the table. (Hint: what are the
requirements for a probability distribution?)
0
0.532
1
0.124
2
0.013
(b)
Find the
probability that x is at least 2 , that is find
P(x ≥ 2).
3
0.055
4
0.129
5
(c)...

a biased coin tossed four times P(T)=2/3 x is number
of tails observed
construct the table of probabulity function f(x) and cumulative
distributive function F(x)
and the probability that at least on tail is observed ie
P(X>1)

X is a discrete random variable representing number of
conforming parts in a sample and has following probability mass
function
?(?) = { ?(5 − ?) if ? = 1, 2, 3, 4
0 otherwise
i) Find the value of constant ? and justify your answer
. ii) ( Determine the cumulative distribution function of X, (in
the form of piecewise function).
iii) Use the cumulative distribution function found in question
2 to determine the following:
a) ?(2 < ?...

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