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3 years ago

14

harmony has twice as many stickers as travis. they have 24 altogether. how many does harmony have? I need the step by step instr

uctions

1 answer:

yaroslaw [1]3 years ago

3 0

First you divide 24 by 3 then your answer should be 8 then you do 8x2 so the answer is 16

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3 years ago

(1 point) An insurance company offers its policyholders a number of different premium payment options. For a randomly selected p

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a)

X | 1 3 5 7

f(X) | 0.4 0.2 0.2 0.2

b) $P(4$

Step-by-step explanation:

For this case we have defined the cumulative distribution function like this:

$F(X) = 0, x$

$F(X) = 0.4, 1 \leq x$

$F(X) = 0.6, 3 \leq x$

$F(X) = 0.8, 5 \leq x$

$F(X) = 1, x \geq 7$

And we know that the general definition for the distribution function is given by:

$F(x) = P(X \leq x) = \sum_{i\leq k} f(i)$

Where f represent the density function.

Part a

For this case we need to find the density function, so we can find the values for the density for each value of X = 1,2,3,4,5,6,7,... since X is a discrete random variable.

$f(1) = P(X=1) = P(X \leq 1) - P(X=0) = F(1) -F(0) = 0.4-0=0.4$

$f(2) = P(X=2) = P(X \leq 2) - P(X=0)- P(X=1) = F(2) -F(1) = 0.4-0.4=0$

$f(3) = P(X=3) = P(X \leq 3) - P(X=0)- P(X=1) -P(X=2) = F(3) -F(2) = 0.6-0.4=0.2$

$f(4) = P(X=4) = P(X \leq 4) - P(X=0)- P(X=1) -P(X=2)-P(X=3) = F(4) -F(3) = 0.6-0.6=0$

$f(5) = P(X=5) = P(X \leq 5) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4) = F(5) -F(4) = 0.8-0.6=0.2$

$f(6) = P(X=6) = P(X \leq 6) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4)-P(X=5) = F(6) -F(5) = 0.8-0.8=0$

$f(7) = P(X=7) = P(X \leq 7) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4)-P(X=5)-P(X=6) = F(7) -F(6) = 1-0.8=0.2$

And for any value higher than 7 we have that:

$x_i \in [8,9,10,...]$

$f(x_i) = F(X_i) -F(X_i -1) = 1-1=0$

So then we have our density function defined like this:

X | 1 3 5 7

f(X) | 0.4 0.2 0.2 0.2

Part b

For this case we want to find this probability $P(4$

And since the random variable is discrete we can write this like that:

$P(4$

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