Statistics Week 10 Graded Assignments

by Khushi Dii
August 12, 2023August 12, 2023
Foundation Graded Assignments

Statistics Week 10 graded assignment Complete Solutions Key Given In This Page Check Below . We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons If Not Able To Complete Graded Assignments

There are

2^{6}

numbered cards in a deck among which

^{6} �_{�}

cards bear the number

�; � = 0, 1, 2, . . ., 6

. From the deck, 10 cards are drawn with replacement. What is the expectation of the sum of their numbers?(Enter the answer correct to 1 decimal accuracy)

1 point

An unbiased die is thrown 13 times. After each throw a ‘+’ is recorded for 2 or 5 and ‘-‘ is recorded for 1,3,4 or 6, the signs forming an ordered sequence. To each, except the first and last sign, a random variable

�_{�}; � = 1, 2, . . ., 11

is associated which takes the value

1

if both of its neighbouring sign differs from the one between them and

0

otherwise. If the random variable

�

is defined as

� = 3 � + 13

where,

� = \sum_{� = 1}^{11} �_{�}

.
Find the expected value of

�

\frac{183}{9}

\frac{139}{9}

\frac{22}{9}

\frac{66}{9}

1 point

�_{�}; � = 1, 2, . . ., 11

is associated which takes the value

1

if both of its neighbouring sign differs from the one between them and

0

otherwise. If the random variable

�

is defined as

� = 3 � + 13

where,

� = \sum_{� = 1}^{11} �_{�}

.
Which of the following statement(s) is/are true?

� (�) = 3 � (�) + 13

� (�) = 9 � (�)

� (�) = 9 � (�) + 13

� (�) = 9 � (�) + 13

1 point

Amandeep is in the middle of a bridge of infinite length. He takes the unit step to the right with probability 0.66 and to the left with probability 0.34. Assume that the movements are independent of each other.
Hint: Consider the random variable

�_{�}

associated with the

�^{� ℎ}

step defined as:

�_{�}

{\begin{cases} 1 & if the step of Amandeep is towards the right \\ - 1 & if the step of Amandeep is towards the left \end{cases}

What is the expected distance between the starting point and end point of Amandeep after 5 steps?

- 0.32

1.6

- 1.6

0.32

1 point

�_{�}

associated with the

�^{� ℎ}

step defined as:

�_{�}

{\begin{cases} 1 & if the step of Amandeep is towards the right \\ - 1 & if the step of Amandeep is towards the left \end{cases}

What is the variance distance between the starting point and end point of Amandeep after 5 steps?

4.49

0.9

1.56

1

A box contains 10 white and 6 black balls. 2 balls are drawn at random without replacement. Find the expected value of the number of white balls drawn. (Enter the answer correct to 2 decimal places)

1 point

Rohit wants to open his door with

5

keys(out of which

1

will open the door) and tries the keys independently and at random. If unsuccessful keys are eliminated from further selection, then Find the expected number of trials required to open the door.
Hint: Suppose Rohit gets the first success at

�^{� ℎ}

trial, i.e., he is unable to open the door in the first

(� - 1)

trials.
And, P(he gets first success at second trial)=

(1 - \frac{1}{5}) \times \frac{1}{4}

�

and

�

are independent random variables with means 14 and 20, and variances 2 and 6 respectively. Find the variance of

3 � + 6 �

1 point

Table Q10.1.G. represents the probability mass function of a random variable X

Table Q10.1.G: Probability Mass Function
$�$	-1	4	5
$� (� = �)$	$\frac{1}{6}$	$\frac{1}{3}$	$\frac{9}{18}$

Calculate the value of

� (2 � + 1)^{2}

. (Enter the answer correct to 2 decimal places)

1 point

Suppose that

�

is a random variable for which

� (�) = 15

and

� � � (�) = 22

. Find the positive values of

�

and

�

such that

� = � � - �

, has expectation

0

and variance

1

\frac{- 1}{\sqrt{22}}

\frac{- 15}{\sqrt{22}}

1

15

\frac{1}{22}

\frac{15}{\sqrt{22}}

\frac{1}{\sqrt{22}}

\frac{15}{\sqrt{22}}

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Statistics Week 10 Graded Assignments

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