If x is a binomial random variable, compute P(x) for each of the following cases:
(a) P(x≤5),n=7,p=0.3
P(x)=
(b) P(x>6),n=9,p=0.2
P(x)=
(c) P(x<6),n=8,p=0.1
P(x)=
(d) P(x≥5),n=9,p=0.3
P(x)=
If x is a binomial random variable, compute p(x) for each of the
following cases:
(a) n=3,x=2,p=0.9 p(x)=
(b) n=6,x=5,p=0.5 p(x)=
(c) n=3,x=3,p=0.2 p(x)=
(d) n=3,x=0,p=0.7 p(x)=
If x is a binomial random variable, compute P(x) for each of the
following cases, rounded to two decimal places:
c) P(x<1),n=5,p=0.1
d) P(x≥3),n=4,p=0.5
If x is a binomial random variable, compute the mean, the
standard deviation, and the variance for each of the following
cases:
(a) n=3,p=0.9
μ=
σ^2=
σ=
(b) n=6,p=0.1
μ=
σ^2=
σ=
(c) n=4,p=0.6
μ=
σ^2=
σ=
(d) n=5,p=0.8
μ=
σ^2=
σ=
Determine whether or not the random variable X is a binomial
random
variable.
(a)
X is the number of dots on the top face of a fair die
(b)
X is the number of hearts in a five card hand drawn (without
replacement) from a well
shuffled ordinary deck.
(c)
X is the number of defective parts in a sample of ten randomly
selected parts coming from a manufacturing process in which 0.02%
of all parts are defective.
(d)
X...
Determine whether or not the random variable X is a binomial
random variable. If so, give the values of n and p. If not, explain
why not.
a. X is the number of dots on the top face of fair die that is
rolled.
b. X is the number of hearts in a five-card hand-drawn (without
replacement) from a well-shuffled ordinary deck.
c. X is the number of defective parts in a sample of ten randomly
selected parts coming from...
Expectation 1
Compute E(X) for the following random variable X
: X=Number of tosses until getting 4 (including the last toss)
by tossing a fair 10-sided die.
E(X)= ?
Expectation 2
Compute E(X) for the following random variable X : X=Number of
tosses until all 10 numbers are seen (including the last toss) by
tossing a fair 10-sided die.
To answer this, we will use induction and follow the steps
below:
Let E(i) be the expected number of additional tosses...
If x is a binomial random variable, use the binomial
probability table to find the probabilities below.
a. P(x<6) for n = 15, p=0.2
b. P(x>=14) for n=20, p=0.8
c. P(x=23) for n=25, p=0.1
If x is a binomial random variable, use the binomial
probability table to find the probabilities below.
a. P(x=3) for n=10, p=0.5
b. P(x≤4) for n=15, p=0.3
c. P(x>1) for n=5, p=0.2
d. P(x<6) for n=15, p=0.8
e. P(x≥14) for n=25, p=0.8
f. P(x=3) for n=20, p=0.1