![subject](/tpl/images/cats/mat.png)
Suppose in a region in california, the intensity of the next earthquake is a random variable y that has an exponential distribution with parameter λ. conditional on y = y, the number of injuries in that region denoted by the random variable x has a poisson distribution with parameter αy where α is another constant. find e(x) and var(x).
![ansver](/tpl/images/cats/User.png)
![ansver](/tpl/images/cats/User.png)
answer: i don't understand it
step-by-step explanation: sorry
![ansver](/tpl/images/cats/User.png)
step-by-step explanation:
step 1: solve one of the equations for one of the variables. let's solve the first equation for y:
step 2: substitute that equation into the other equation, and solve for x.
step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.
![ansver](/tpl/images/cats/User.png)
x =-.20752
step-by-step explanation:
4^(x+2)=12
4^(x+2)=12
take the log base 4 on each side
log 4 (4^(x+2) = log 4(12)
we know log b(a^y) = y log b (a)
(x+2) log 4(4) = log 4 (12)
x+2 = log 4 (12)
we know logb c = loga c/loga b
we want to convert to base 10 so a = 10
by default, we do not write the 10 c = 4 and b = 10
log4 10 = log 12/log 4
log4 10 = log 12/ log 4
x+2 = log 12/ log 4
subtract 2 from each side
x +2 -2 = log 12/ log 4 -2
x = 1.79248125 -2
x =-.20752
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