The lifetime, in years, of some electronic component is a continuous random variable with the density f(x) =   k x4 for x ≥ 1 0 for x < 1. Find k, the cumulative distribution function, and the probability for the lifetime to exceed 2 years.

I suppose the density is supposed to be

(since diverges as , and 0 is conveniently left out of the domain)

For this to be a proper density function, it must be positive (it is) and its integral over the support must evaluate to 1. We have

which means .

The distribution function is obtained by integrating the density:

The probability that the component exceeds 2 years in its lifetime is

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?