14 Σ [(1.3^n) * (150)]n = 0
Using the sigma notation to find the sum of his first 15 payments, each of the possible values of n (from 0 to 14) are substituted into the equation. After which, each of the results are then added to each other. Also, the problem states that only the first 15 payments are to be included in the notation. This shows that the series is limited and is finite. Therefore, it is a convergent series.
Answer:
Refer below
Step-by-step explanation:
a) a and b are the lower and higher values of the interval for which uniform distribution is defined.
Here a= 6 and b =10
b) Mean of the uniform distribution= (a+b)/2 = (6+10)/2 =8
Or int x (1/4) dx = x^2/8 = 8
c) Variance of the uniform distribution = (b^2-a^2)/12 = (100-64)/12
= 36/12 =3
Std dev = sq rt of 3 = 1.732
d) To find total area
PDF of the distribution = 1/(b-a) = 1/4, 6<x<10
Area = \int 6 to 10 of 1/4 dx
= x/4
Subtitute limits
= (10-6)/4 =1
So total area = 1
d)P(X>7) = int 7 to 10 of 1/4 dx = 3/4
e) P(7<x<9) = Int 7 to 9 of 1/4 dx = 2/4 = 1/2
The expanded answer is 2025m^2+1620m+324
I hope this helps you out! Take care
