Could I get solved answers to parts c and d? Thank you Not to be collected, but

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Could I get solved answers to parts c and d? Thank you Not to be collected, but should be completed by start of class on Wednesday March 22 The following observations were collected: 8.14, -0.37, -1.56, and 0.93 a). Calculate the mid-points to be used for an empirical continuous CDF. b). Assign the endpoints a_0 and a_n in such a way that the distance from these endpoints to the nearest observation points is exactly twice as long as the distance from the observation points to the closest midpoint. For example, if the min observed value (X_(1)) the first midpoint (a_f) is 4, then a_0 should be 1 = 3 - 2*(4-3). c). Write the pdf and CDF of the empirical distribution for this specific problem (make sure that your CDF and pdf are written in a way that they can be evaluated at any point with a simple calculation. d). Calculate the following from the empirical distribution: P {X lessthanorequalto 0} = P {X > 3} = P {0

Explanation / Answer

data points are

8.14,-0.37,-1.56,0.93

so the mean and standard deviation are

mean = 1.785

sd = 4.35

now using the z score formula z = (X- mean) /sd , we conver the x values into z scores and shall then use z tables to find the probabilites. Please keep the z table handy with you

P(X<=0) = (0 - 1.785)/4.35 = -0.410

P(Z<-0.410) =

P ( Z<0.410 )=1P ( Z<0.41 )=10.6591=0.3409

######

P(X>3) = (3 - 1.785)/4.35 = 0.2793

P ( Z>0.2793 )=1P ( Z<0.2793 )=10.6103=0.3897

#####

P(0<X<1)

P(X<0) = (0 - 1.785)/4.35 = -0.410

P(X<1) = (1 - 1.785)/4.35 = -0.1804

again using the z table we find

P(-0.410 <z<-0.1804)

To find the probability of P (0.410<Z<0.1804), we use the following formula:

P (0.410<Z<0.1804 )=P ( Z<0.1804 )P (Z<0.410 )

P ( Z<0.1804 ) can be found by using the following fomula.

P ( Z<a)=1P ( Z<a )

After substituting a=0.1804 we have:

P ( Z<0.1804)=1P ( Z<0.1804 )

We see that P ( Z<0.1804 )=0.5714 so,

P ( Z<0.1804)=1P ( Z<0.1804 )=10.5714=0.4286

P ( Z<0.410 ) can be found by using the following fomula.

P ( Z<a)=1P ( Z<a )

After substituting a=0.41 we have:

P ( Z<0.410)=1P ( Z<0.41 )

We see that P ( Z<0.41 )=0.6591 so,

P ( Z<0.410)=1P ( Z<0.41 )=10.6591=0.3409

At the end we have:

P (0.410<Z<0.1804 )=0.0877

Ex for the data points is the mean value which is

mean = 1.785

please note we can answer 4 parts of a mulitple parts question , I have answered D in full

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