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3 years ago

S2 Summer Holiday Homework

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

6 0

I. xy + 2y=3 Not linear equation because is grade 2 equation (xy).

II. x-2y = y Are linear equations in two unknowns (x and y).

III. 3x + 2y = 5 Are linear equations in two unknowns (x and y).

<h2>Corect ansver: C) II and III only</h2><h2></h2>

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A standard deck of 52 cards contains 4 suits: hearts, clubs, diamonds, and spades. Each suit contains cards numbered 2 through 1

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Step-by-step explanation:

Number of cards in a standard deck = 52

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Number of 6's = 4 (1 for each suit)

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Step-by-step explanation:

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2 years ago

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Seven thousand lottery tickets are sold for $5 each. One ticket will win $2,000, two tickets will win $750 each, and five ticket

Keith_Richards [23]

Answer:

a) The distribution for the random variable X is given by:

X | -5 | 95 | 745 | 1995 |

P(X) | 6992/7000 | 5/7000 | 2/7000 | 1/7000 |

b) E(X)=-4.43. That means if we buy an individual ticket by $5 on this lottery the expected value of loss if $4.43.

c) $Sd(X)=\sqrt{Var(X)}=\sqrt{738.947}=27.184$

Step-by-step explanation:

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).

And the standard deviation of a random variable X is just the square root of the variance.

Part a

The info given is:

N=7000 represent the number of tickets sold

$5 is the price for any ticket

Number of tickets with a prize of $2000 =1

Number of tickets with a prize of $750=2

Number of tickets with a prize of $100=5

Let X represent the random variable net gain when we buy an individual ticket. The possible values that X can assume are:

___________________________

Ticket price Prize Net gain (X)

___________________________

5 2000 1995

5 750 745

5 100 95

5 0 -5

___________________________

Now we can find the probability for each value of X

P(X=1995)=1/7000, since we ave just one prize of $2000

P(X=745)=2/7000, since we have two prizes of $750

P(X=95)=5/7000, since we have 5 prizes of $100

P(X=-5)=6992/7000. since we have 6992 prizes of $0.

So then the random variable is given by this table

X | -5 | 95 | 745 | 1995 |

P(X) | 6992/7000 | 5/7000 | 2/7000 | 1/7000 |

Part b

In order to calculate the expected value we can use the following formula:

$E(X)=\sum_{i=1}^n X_i P(X_i)$

And if we use the values obtained we got:

$E(X)=(-5)*(\frac{6992}{7000})+(95)(\frac{5}{7000})+(745)(\frac{2}{7000})+(1995)(\frac{1}{7000})=\frac{-31000}{7000}=-4.43$

That means if we buy an individual ticket by $5 on this lottery the expected value of loss if $4.43.

Part c

In order to find the standard deviation we need to find first the second moment, given by :

$E(X^2)=\sum_{i=1}^n X^2_i P(X_i)$

And using the formula we got:

$E(X^2)=(25)*(\frac{6992}{7000})+(9025)(\frac{5}{7000})+(555025)(\frac{2}{7000})+(3980025)(\frac{1}{7000})=\frac{5310000}{7000}=758.571$

Then we can find the variance with the following formula:

$Var(X)=E(X^2)-[E(X)]^2 =758.571-(-4.43)^2 =738.947$

And then the standard deviation would be given by:

$Sd(X)=\sqrt{Var(X)}=\sqrt{738.947}=27.184$

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Step-by-step explanation:

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