Math, asked by nandinimukherjee777, 8 months ago

The mean of uniform distribution with parameter a and b is

(a) b-a (b)b+a (c) (a+b)/2 (d) (b-a)/2

Answers

Answered by mohansah986
0

Answer:

The notation for the uniform distribution is X ~ U(a, b) where a = the lowest value of x and b = the highest value of x.

The probability density function is

f

(

x

)

=

1

b

a

f(x)=1b−a for a ≤ x ≤ b.

For this example, X ~ U(0, 23) and

f

(

x

)

=

1

23

0

f(x)=123−0 for 0 ≤ X ≤ 23.

Formulas for the theoretical mean and standard deviation are

μ

=

a

+

b

2

and

σ

=

(

b

a

)

2

12

μ=a+b2andσ=(b−a)212

For this problem, the theoretical mean and standard deviation are

μ

=

0

+

23

2

=

11.50

seconds

and

σ

=

(

23

0

)

2

12

=

6.64

seconds

μ=0+232=11.50 secondsandσ=(23−0)212=6.64 seconds

Notice that the theoretical mean and standard deviation are close to the sample mean and standard deviation in this example.

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