Question

Construct the discrete probability distribution for the random variable described. Express the probabilities as simplified fractions. The number of tails in 5 tosses of a coin.

Answer #1

**Solution:**

The number of heads possible in 5 tosses of a coin are 0,1,2,3,4,5

The total number of outcomes are

Now we will get following Probability distribution:

(Head, Probability)

0 ,1/32 ----------------> All tails {TTTTT}

1 ,5/32 --------------> {HTTTT}, {THTTT},{TTHTT},{TTTHT},
{TTTTH} and so on....

2 ,10/32 (or 5/16)

3 ,10/32 (or 5/16)

4 ,5/32

5 ,1/32

The Probability distribution is

X | 0 | 1 | 2 | 3 | 4 | 5 |

P(X) |

Construct the discrete probability distribution for the random
variable described. Express the probabilities as simplified
fractions.
The number of heads in 5 tosses of a coin.

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. Given a discrete random variable, X , where the
discrete probability distribution for X is given on right,
calculate E(X)
X
P(X)
0
0.1
1
0.1
2
0.1
3
0.4
4
0.1
5
0.2
2. Given a discrete random variable, X , where the
discrete probability distribution for X is given on right,
calculate the variance of X
X
P(X)
0
0.1
1
0.1
2
0.1
3
0.4
4
0.1
5
0.2
3. Given a discrete random variable, X...

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[?].

Let W be a random variable giving the number of
tails
minus the number of
heads
in three tosses of a coin. Assuming that a
tail
is
half
as likely to occur, find the probability distribution of the
random variable W.
Complete the following probability distribution of W.

A discrete random variable can be described by the
binomial distribution if it satisfies four conditions, state these
4 conditions

What kind of variable has values determined by chance?
random variable
discrete variable
continuous variable
Question 5
A binomial distribution is a probability distribution for a:
discrete random variable
continuous random variable
Question 6
A normal distribution is a probability distribution for a:
continuous random variable
discrete random variable
Question 7
Which is not a property of the binomial distribution?
only two outcomes
fixed number of trials
constant probability of success
dependent outcomes

The values that a discrete random variable, X, can take are
1,2,3,4 with the probabilities 0.19, 0.22, 0.21, 0.38 respectively.
Find the mean and variance of the probability distribution.
Group of answer choices
2.58, 1.10
2.78, 1.34
2.61, 1.04
2.61, 1.10

A discrete random variable, X, takes on the values
8, 125, 750, and 3,800, with probabilities
0.70, 0.15, 0.10, 0.05, respectively. Use the
statistical capacity of your calculator to find the
standard deviation of the random variable,
X, rounded to two decimal places. Note that this is a
probability distribution.
Your Answer:

Problem 3. Let x be a discrete random variable with the
probability distribution given in the following table:
x = 50 100 150 200 250 300 350
p(x) = 0.05 0.10 0.25 0.15 0.15 0.20 0.10
(i) Find µ, σ 2 , and σ.
(ii) Construct a probability histogram for p(x).
(iii) What is the probability that x will fall in the interval
[µ − σ, µ + σ]?

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