Free Printable SM025 DISCRETE RANDOM VARIABLES

1.

Refer to question 3 about 2 dice..

Find P(x>5).

a)

1/9

b)

1/10

c)

1/11

d)

1/12

2.

Refer to question 2 about biased dice..

Find P(X<3).

a)

1/2

b)

1/3

c)

1/4

d)

1/5

3.

The total probability of a continuous random variable is ...

a)

MUST equal 1

b)

MUST less than 1

c)

MUST bigger than 1

d)

MUST in between 0 to 1

4.

The random variable X has probability function $P\left(X=x\right)=kx\ \ for\ x=1,2,3,4,5$ . Find k.

a)

$\frac{1}{5}$

b)

$\frac{1}{10}$

c)

$\frac{1}{15}$

d)

$\frac{1}{14}$

5.

$P\left(4<X<10\right)=F\left(9\right)-F\left(4\right)$

a)

FALSE

b)

TRUE

6.

$P\left(X<7\right)=1-P\left(X\ge6\right)$

a)

FALSE

b)

TRUE

7.

The random variable X has probability function $P\left(X=x\right)=\frac{\left(2x-1\right)}{36}\ \ for\ x=1,2,3,4,5,6$

Find $P\left(X=3\right)$

a)

$\frac{1}{12}$

b)

$\frac{7}{36}$

c)

$\frac{1}{6}$

d)

$\frac{5}{36}$

8.

$P\left(-2\le T<7\right)\$ is equal to

a)

$F\left(7\right)-F\left(-2\right)$

b)

$F\left(6\right)-F\left(-3\right)$

c)

$F\left(8\right)-F\left(-3\right)$

d)

$F\left(6\right)-F\left(-2\right)$

9.

If the expected value is negative, are you expected to win?

a)

YES

b)

NO

10.

Given the probability model below, what is the expected value of the random variable?

$\ \ \ \ x\ \ \ \ \ \ \ \ \ \ \ \ \ \ 50\ \ \ \ \ \ 20\ \ \ \ \ \ 5$

$P\left(X=x\right)\ \ \ 0.1\ \ \ 0.3\ \ \ 0.6$

a)

4.67

b)

5

c)

14

d)

7.5

11.

How many possible outcomes will appear if you roll a common dice?

a)

12

b)

6

c)

1

d)

36

12.

Those are properties of variance except

a)

$Var\ (a)=0$

b)

$Var\ (aX)=a^2\ Var\ \left(X\right)$

c)

$Var\left(aX+b\right)=Var\left(X\right)+b$

d)

$Var\left(aX+b\right)=a^2Var\left(X\right)$

13.

The random variable X has probability distribution.

Given that E(X) = 3.5, find p and q.

a)

p = 0.15 q = 0.25

b)

p = 0.05 q = 0.35

c)

p = 0.3 q = 0.1

d)

p = 0.2 q = 0.2

14.

E(X) = 3.5, find E(X²).

a)

14.25

b)

12.25

c)

12

d)

14

15.

E(X) = 3.5, E(X²) = 14. Find Var(X).

a)

1.25

b)

1.75

c)

1.35

d)

1

16.

E(X) = 3.5, find E(3 - 2X)

a)

-4

b)

2

c)

-7

d)

0.5

17.

Var(X) = 1.75, find Var(2X - 1).

a)

2

b)

7

c)

1.5

d)

2.5

18.

Two fair dice are tossed together three times. Let X be a discrete random variable for getting less than 6 from the sum of the numbers on the two dice. Write the values of X in a set notation.

a)

X = {0, 1, 2, 3}

b)

X = {0, 1, 2, 3,4,5,6}

c)

X = {1, 2, 3,4,5,6}

d)

X = {1, 2, 3,4,5,6,7,8,9,10,11,12}

19.

Two fair dice are tossed together three times. Let X be a discrete random variable for getting less than 6 from the sum of the numbers on the two dice. What is the probability of getting less than 6 in each trial?

a)

$\frac{1}{6}$

b)

$\frac{1}{36}$

c)

$\frac{5}{18}$

d)

$\frac{5}{36}$

20.

Two fair dice are tossed together three times. Let X be a discrete random variable for getting less than 6 from the sum of the numbers on the two dice.

Select the correct statement(s).

a)

$P\left(X=0\right)=\frac{2197}{5832}$

b)

$P\left(X=1\right)=\frac{845}{5832}$

c)

$P\left(X=2\right)=\frac{325}{1944}$

d)

$P\left(X=3\right)=\frac{125}{5832}$

21.

Two fair dice are tossed together three times. Let X be a discrete random variable for getting less than 6 from the sum of the numbers on the two dice.

The total probability for the distribution of X is 1.

a)

True

b)

False

22.

A discrete random variable X has the probability distributions shown in the table. Find the value of k. (Remember that a valid probability distribution must add up to 1)

a)

1/3

b)

7/12

c)

1/12

d)

1/4

23.

Given the probability model in the table below, what is the expected value of the random variable?
X 50 20 5
P(X) 0.1 0.3 0.6

a)

14

b)

4.67

c)

5

d)

7.5

24.

Find the value of k

a)

¹/₁₅

b)

¹/₅

c)

¹/₁₀

d)

¹/₁₄

25.

Find the value of k

a)

¹/₁₅

b)

¹/₁₆

c)

¹/₁₇

d)

¹/₁₄

26.

Find P(X = 2)

a)

⁵/₃₆

b)

¹/₁₂

c)

¹/₃₆

d)

¹/₉

27.

Find the value of q

a)

0.85

b)

0.15

c)

0.25

d)

0.05

28.

Find P(X < 5)

a)

0.2

b)

0.3

c)

0.5

d)

0.7

29.

Which statement is true?

a)

5a + b = 1

b)

6a + b = 1

c)

5a + 2b = 1

d)

7a + b = 1

30.

Find a if b = 0.4

a)

0.1

b)

0.2

c)

0.4

d)

0.6

31.

Find the value of k

a)

¹/₆

b)

¹/₁₄

c)

¹/₁₁

d)

¹/₁₅

32.

The total probability of a discrete random variable is ...

a)

MUST equal 1

b)

MUST less than 1

c)

MUST bigger than 1

d)

MUST in between 0 to 1

33.

How many possible outcomes will appear if you roll a common dice?

a)

12

b)

6

c)

1

d)

36

34.

State whether it is Discrete or Continuous;

The speed of a car

a)

Discrete

b)

Continuous

35.

State whether it is Discrete or Continuous;

The sum rolled on a pair of dice

a)

Discrete

b)

Continuous

36.

$P\left(4<X<10\right)=F\left(9\right)-F\left(4\right)$

a)

FALSE

b)

TRUE

37.

$P\left(X<7\right)=1-P\left(X\ge6\right)$

a)

FALSE

b)

TRUE

38.

$P\left(-2\le T<7\right)\$ is equal to

a)

$F\left(7\right)-F\left(-2\right)$

b)

$F\left(6\right)-F\left(-3\right)$

c)

$F\left(8\right)-F\left(-3\right)$

d)

$F\left(6\right)-F\left(-2\right)$

39.

Determine if the data set is discrete or continuous.

The temperature at noon.

a)

discrete

b)

continuous

40.

The total probability of a discrete random variable is ...

a)

MUST equal 1

b)

MUST less than 1

c)

MUST bigger than 1

d)

MUST in between 0 to 1

41.

The random variable X has probability function $P\left(X=x\right)=kx\ \ for\ x=1,2,3,4,5$ . Find k.

a)

$\frac{1}{5}$

b)

$\frac{1}{10}$

c)

$\frac{1}{15}$

d)

$\frac{1}{14}$

42.

$P\left(4<X<7\right)=P\left(5\le X\le6\right)$

a)

FALSE

b)

TRUE

43.

How many possible outcomes will appear if you roll a common dice?

a)

12

b)

6

c)

4

d)

36

44.

Those are properties of variance except

a)

$Var\ (a)=0$

b)

$Var\ (aX)=a^2\ Var\ \left(X\right)$

c)

$Var\left(aX+b\right)=Var\left(X\right)+b$

d)

$Var\left(aX+b\right)=a^2Var\left(X\right)$

45.

The random variable X has probability function $P\left(X=x\right)=\frac{\left(2x-1\right)}{36}\ \ for\ x=1,2,3,4,5,6$

Find $P\left(X=3\right)$

a)

$\frac{1}{12}$

b)

$\frac{7}{36}$

c)

$\frac{1}{6}$

d)

$\frac{5}{36}$

46.

Find P(X < 5)

a)

0.2

b)

0.3

c)

0.5

d)

0.7

47.

Which statement is true?

a)

5a + b = 1

b)

6a + b = 1

c)

5a + 2b = 1

d)

7a + b = 1

48.

Given that: E(X)=2 E(X^2)=6

a)

37

b)

40

c)

10

d)

7

49.

Given that E(X)=2 and E(X^2)=9.Find the variance of X

a)

-5

b)

5

c)

77

d)

65

50.

Is this a probability distribution?

a)

No, the sum of p(x) does not equal 1.

b)

Yes, all p(x) are between 0 and 1.

c)

No, all p(x) are not between 0 and 1.

d)

Yes, the sum p(x) is 1.

SM025 DISCRETE RANDOM VARIABLES

Total questions: 50

Worksheet time: 1hrs 10mins

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