Question

If *x* is a binomial random variable, compute the mean,
the standard deviation, and the variance for each of the following
cases:

(a)
*n*=4,*p*=0.7

*μ*=

*σ*2=

*σ*=

(b)
*n*=3,*p*=0.7

*μ*=

*σ*2=

*σ*=

(c)
*n*=5,*p*=0.4

*μ*=

*σ*2=

*σ*=

(d)
*n*=5,*p*=0.8

*μ*=

*σ*2=

*σ*=

Answer #1

Solution(a)

Mean of the bionomial distribution = (n*p)= (4*0.7)=2.8

Varinace of bionomial distribution = n*p*q = 4*0.7*0.3 = 0.84

Standard deviation of bionomial distribution = sqrt(variance)= sqrt(0.84)= 0.9165

Solution(b)

Mean = 3*0.7 = 2.1

Variance = 3*0.7*0.3=0.63

Standard deviation = sqrt(0.63)= 0.7937

Solution(c)

Mean = 5*0.4=2

Varinace = 5*0.4*0.6 = 1.2

Standard deviation = sqrt(1.2)= 0.9554

Solution(d)

Mean = 5*0.8= 4

Varinace = 5*0.8*0.2= 0.8

Standard deviation = sqrt(0.8)= 0.8944

If ? is a binomial random variable, compute the mean, the
standard deviation, and the variance for each of the following
cases:
(a) ?=5, ?=0.6
?=
?2=
?=
(b) ?=6, ?=0.3
?=
?2=
?=
(c) ?=4, ?=0.7
?=
?2=
?=
(d) ?=3, ?=0.6
?=
?2=
?=

If ? is a binomial random variable, compute the mean, the
standard deviation, and the variance for each of the following
cases:
(a) ?=4,?=0.8
?=
?2=
?=
(b) ?=5,?=0.3
?=
?2=
?=
(c) ?=6,?=0.9
?=
?2=
?=
(d) ?=5,?=0.9
?=
?2=
?=

1) Suppose a random variable, x, arises from a binomial
experiment. Suppose n = 6, and p = 0.11.
Write the probability distribution. Round to six decimal places,
if necessary.
x
P(x)
0
1
2
3
4
5
6
Find the mean.
μ =
Find the variance.
σ2 =
Find the standard deviation. Round to four decimal places, if
necessary.
σ =
2) Suppose a random variable, x, arises from a binomial
experiment. Suppose n = 10, and p =...

Find the mean, μ, and standard deviation, σ, for a binomial
random variable X. (Round all answers for σ to three decimal
places.)
(a) n = 45, p = .50.
μ =
σ =
(b) n = 1, p = 0.25.
μ =
σ =
(c) n = 100, p = 0.75.
μ =
σ =
(d) n = 30, p = .01.
μ =
σ =

i) A random variable X has a binomial distribution with mean 6
and variance 3.6: Find P(X = 4).
ii) Let X equal the larger outcome when a pair of four-sided
dice is rolled. The pmf of X is
f(x) = (2x - 1/ 16) ; x = 1; 2; 3; 4.
Find the mean, variance and standard deviation of X.
iii) Let μ and σ^2 denote the mean and variance of the random
variable able X. Determine E [(X...

If x is a binomial random variable, compute P(x) for each of the
following cases:
(a) P(x≤4),n=6,p=0.9
P(x)=
(b) P(x>2),n=6,p=0.7
P(x)=
(c) P(x<2),n=3,p=0.1
P(x)=
(d) P(x≥1),n=7,p=0.3
P(x)=

X is a binomial random variable with the parameters shown. Use
the special formulas to compute its mean μ and standard deviation
σ.
1. n = 8, p = 0.43
2. n = 47, p = 0.82
3. n = 1200, p = 0.44
4. n = 2100, p = 0.62

1. If X is a binomial random variable, compute for each of the
following cases:
a) n=15, p= 0.4 , P(5<= X < 9)
b) n=9, p=0.2, P(X >= 2)

if x is a binomial random variable, compute P(x) for each of the
following cases (record your answer to atleast 3 decimal
places):
(a) P(x≤1),n=3,p=0.5
P(x)=?
(b) P(x>4),n=8,p=0.6
P(x)= ?
(c) P(x<4),n=6,p=0.7
P(x)= ?
(d) P(x≥3),n=7,p=0.3
p(x)=?

If ?x is a binomial random variable, compute ?(?) for each of
the following cases:
(a) ?(?≤6),?=8,?=0.2
?(?)=
(b) ?(?>4),?=5,?=0.5
?(?)=
(c) ?(?<2),?=3,?=0.8
?(?)=
(d) ?(?≥5),?=9,?=0.6
?(?)=

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