Question

**Question 1**

Refer to the probability function given in the following table
for a

random variable X that takes on the values 1,2,3 and 4

X 1 2 3 4

P(X=x) 0.4 0.3 0.2 0.1

**a)** Verify that the above table meet the conditions
for being a discrete probability

distribution

**b)** Find P(X<2)

**c)** Find P(X=1 and X=2)

**d)** Graph P(X=x)

**e)** Calculate the mean of the random variable
X

**f)** Calculate the standard deviation of the random
variable X

**Question 2**

Graph P(X=x) for binomial distributions with the following
parameters

**a)** ? = 4 ??? ? = 0.5

**b)** ? = 4 ??? ? = 0.3

**c)** ? = 4 ??? ? = 0.1

**d)** Which if any of the graphs in part a-c are
symmetric?

**e)** Without actually constructing the graph, would
the case

? = 10 ??? ? = 0.5 be symmetric or skewed?

**f)** Which of the graphs in part a-c is the most
heavily skewed?

**g)** Without actually constructing the graph, would
the case ? = 4 and

? = 0.01 exhibit more or less skewness than the graph in
part(c)?

**Question 3**

Suppose that a random variable y has a Poisson
distribution.

Compute the following probabilities

**a)** P(y = 4) given ? = 3

**b)** P(y<4) given ? = 3

**c)** P(y<=4) given ? = 3

**d)** P(y>4) given ? = 3

**e)** P(2<y<5) given ? = 3

**Question 4**

The number of calls coming to the customer care center of a
mobile company per

minute is a Poisson random variable with mean 5. Find the
probability that no call

comes in a certain minute

Answer #1

**Question 1**

Refer to the probability function given in the following table
for a

random variable X that takes on the values 1,2,3 and 4

X 1 2 3 4

P(X=x) 0.4 0.3 0.2 0.1

**a)** Verify that the above table meet the conditions
for being a discrete probability

distribution

**b)** Find P(X<2)

**c)** Find P(X=1 and X=2)

**d)** Graph P(X=x)

**e)** Calculate the mean of the random variable
X

**f)** Calculate the standard deviation of the random
variable X

a)If sum of all probabilities is one then we say that it is discrete probability distribution.

x | P(x) |

1 | 0.4 |

2 | 0.3 |

3 | 0.2 |

4 | 0.1 |

Total | 1 |

b)

P(X < 2) = P(X = 1) = 0.4

c)

P(X = 1 and X = 2) = P(X = 1)*P(X = 2) = 0.4*0.3 = 0.12

d)

The graph of P(X = x)

e)

The mean of the random variable X is:

x | P(x) | x*P(X) |

1 | 0.4 | 0.4 |

2 | 0.3 | 0.6 |

3 | 0.2 | 0.6 |

4 | 0.1 | 0.4 |

Total | 1 | 2 |

f) The standard deviation of random variable X:

x | P(x) | x*P(X) | x^2*P(x) |

1 | 0.4 | 0.4 | 0.4 |

2 | 0.3 | 0.6 | 1.2 |

3 | 0.2 | 0.6 | 1.8 |

4 | 0.1 | 0.4 | 1.6 |

Total | 1 | 2 | 5 |

----------------------------------------------------------------------------------------------------------------

For the remaining questions please repost!

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)

Determine whether or not the table is a valid probability
distribution of a discrete random variable. Explain fully.
a.
x
-2
0
2
4
P(x)
0.3
0.5
0.2
0.1
b.
x
0.5
0.25
0.25
P(x)
-0.4
0.6
0.8
c.
x
1.1
2.5
4.1
4.6
5.3
P(x)
0.16
0.14
0.11
0.27
0.22

A random variable has the probability distribution table as
shown. Calculate P(X≤1).
x -3 | -2 | -1 | 0 | 1
P (X = x) | - | - | 0.3 | 0.1 | 0.1

Suppose that the random variable X has the following cumulative
probability distribution
X: 0 1. 2. 3. 4
F(X): 0.1 0.29. 0.49. 0.8. 1.0
Part 1: Find P open parentheses 1 less or equal than
x less or equal than 2 close parentheses
Part 2: Determine the density function f(x).
Part 3: Find E(X).
Part 4: Find Var(X).
Part 5: Suppose Y = 2X - 3, for all of X, determine
E(Y) and Var(Y)

In each part, assume the random variable ?X has a binomial
distribution with the given parameters. Compute the probability of
the event.
(a) ?=6,?=0.5
??(?=3)=
(b) ?=6,?=0.1
??(?=2)=
(c) ?=4,?=0.7
??(?=2)=
(d) ?=4,?=0.5
??(?=3)=

The random variable X can take on the values 1, 2 and 3
and the random variable Y can take on the values 1, 3, and 4. The
joint probability distribution of X and Y is given in the following
table:
Y
1
3
4
X
1
0.1
0.15
0.1
2
0.1
0.1
0.1
3
0.1
0.2
a. What value should go in the blank cell?
b. Describe in words and notation the event
that has probability 0.2 in...

A random variable x has the following probability distribution.
Determine the standard deviation of x.
x
f(x)
0
0.05
1
0.1
2
0.3
3
0.2
4
0.35
A random variable x has the following probability distribution.
Determine the expected value of x.
x
f(x)
0
0.11
1
0.04
2
0.3
3
0.2
4
0.35
QUESTION 2
A random variable x has the following probability distribution.
Determine the variance of x.
x
f(x)
0
0.02
1
0.13
2
0.3
3
0.2...

1. Let X be a discrete random variable with the probability mass
function P(x) = kx2 for x = 2, 3, 4, 6.
(a) Find the appropriate value of k.
(b) Find P(3), F(3), P(4.2), and F(4.2).
(c) Sketch the graphs of the pmf P(x) and of the cdf F(x).
(d) Find the mean µ and the variance σ 2 of X. [Note: For a
random variable, by definition its mean is the same as its
expectation, µ = E(X).]

The following table denotes the probability distribution for a
discrete random variable X.
x
-2
0
1
2
9
p(x)
0.1
0.3
0.2
0.3
0.1
The standard deviation of X is closest to
Group of answer choices
3.74
4.18
2.77
7.65
11

The probability distribution of a random variable X is
given.
x
−4
−2
0
2
4
p(X =
x)
0.2
0.1
0.3
0.2
0.2
Compute the mean, variance, and standard deviation of
X. (Round your answers to two decimal places.)
Find mean, variance, and standard deviation

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