Question

Let X ∼ B(5, 0.3). Determine:

(b) P(X < 2);

(c) P(X > 2);

Let X ∼ P0(2.1). Determine:

(a) P(X = 5);

(b) P(X < 3);

(c) P(X ≥ 3);

(d) E(X);

(e) var(X).

Answer #1

since X ∼ B(5, 0.3) , this means X is binomial distribution with parameter n=5 and p=0.3 and

for Binomial distribution
,P(X=r)=^{n}C_{r}p^{r}(1-p)^{n-r}

(b) P(X < 2)=P(X<=1)=0.5282 ( using ms-excel =BINOMDIST(1,5,0.3,1) )

(c) P(X > 2)=1-P(X<=2)=1-0.8369=0.1631

P(X<=2)=0.8369 ( =BINOMDIST(2,5,0.3,1) )

X ∼ P0(2.1), here X is poisson distribution with parameter =2.1 and

for Poisson distribution, P(X=x)=exp(-λ)λ^^{x}/x!

(a) P(X = 5)= 0.0417 ( =POISSON(5,2.1,0))

(b) P(X < 3)=P(X<=2)= 0.6496 ( =POISSON(2,2.1,1))

(c) P(X ≥ 3)=1-P(X<3)=1-P(X<=2)=1-0.6496=0.3504

(d) E(X)==2.1,

(e) var(X)==2.1

for poisson distribution mean and variance are equal and it is equal to =2.1

Let f(x)=(1/2)(x/5), x=1,2,3,4 Hint: Calculate F(X).
Find; (a) P(X=2) , (b) P(X≤3) , (c) P(X>2.5), (d) P(X≥1), (e)
mean and variance, (f) Graph F(x)

Let P(A) = 0.1, P(B) = 0.2, P(C) = 0.3 and P(D) = 0.4;
A, B, C, D – independent events. Compute P{(A∪B)∩ (Cc ∪
Dc }.
Step by step solution.

91. Let X be a RV with support set {0, 1, 2}, p(1) =
0.3, and p(2) = 0.5. Calculate E[X]. Let X be a discrete RV. Define
the expected value E[X] of X. Is E[X] constant or random?
Why?
92. Suppose X is a RV with support {−1,0,1} where p(−1)
= q and p(1) = p. What relationship must hold between p and q to
ensure that E[X] = 0?
93. Let X be a discrete RV and a,...

13.
Assume A and B are independent events with P(A)= 0.2 and P(B)= 0.3.
let C be the event that none of the events A and B occurs, let D be
the event that exactly one of the events A and B occurs. Find P(A
given D)?

3) Given the events A and B, and P (A) = 0.3, P (B) = .5 and P
(A and B) = .1
Determine:
a) P (A∪B) b) P (A∪Bc) c) P (A / B)
Hint: make the Venn diagram
4) Given events A and B, and P (A) = 0.3, P (B) = .5 If the
events are independent, determine:
a) P (A∪B)
b) P (A∩Bc) c) P ((A∩B) c)
5) If the events are mutually exclusive, determine:
a)...

Let X be a binomial random variable with E(X) = 7 and Var(X) =
2.1.
(a) [5 pts] Find the parameters n and p for the binomial
distribution.
n =
p =
(b) [5 pts] Find P(X = 4). (Round your answer to four decimal
places.)
(c) [5 pts] Find P(X > 12)

Let A and B be two events from the sample space S. Given
P(A)=0.3, P(B)=0.4 and P(A or B)=0.6
Find: a) P(A and B) b) P(not A) c) P(not B) d) P(not(A and B))
e) P(not(A or B))

x
−5
−4
−3
−2
−1
P(X=x)
0.2
0.1
0.3
0.1
0.3
Step 3 of 5 :
Find the standard deviation. Round your answer to one decimal
place.
Step 4 of 5 :
Find the value of P(X> ?5). Round your answer to one decimal
place.
Step 5 of 5 :
Find the value of P(X> ?6). Round your answer to one decimal
place.

Let A and B be events with P (A)= 0.3 and P (B)=0.7, and P (A or
B)=0.9. (a) Compute . (b) Are and mutually exclusive? Explain. (c)
Are and independent? Explain.

Suppose X is a discrete random variable with probability mass
function given by
p (1) = P (X = 1) = 0.2
p (2) = P (X = 2) = 0.1
p (3) = P (X = 3) = 0.4
p (4) = P (X = 4) = 0.3
a. Find E(X^2) .
b. Find Var (X).
c. Find E (cos (piX)).
d. Find E ((-1)^X)
e. Find Var ((-1)^X)

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