1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kirill115 [55]
3 years ago
9

(1 pt) let x be an exponential random variable with parameter \lambda = 4, and let y be the random variable defined by y = 2 e^x

. compute the probability density function of y:
Mathematics
1 answer:
kupik [55]3 years ago
4 0
Y=2e^X\iff X=\ln\dfrac Y2

Note that x\in[0,\infty), so that y\in[2,\infty).

F_Y(y)=\mathbb P(Y\le y)=\mathbb P(2e^X\le y)=\mathbb P\left(X\le\ln\dfrac y2\right)=F_X\left(\ln\dfrac y2\right)

F_X(x)=1-e^{-4x}
\implies F_Y(y)=1-e^{-4\ln\frac y2}=1-\dfrac{16}{y^4}

\implies f_Y(y)=\dfrac{\mathrm dF_Y(y)}{\mathrm dy}=\dfrac{64}{y^5}
You might be interested in
Determine the equation of the circle graphed below.
Bond [772]

Answer:

(x+7)^2+(y-2)^2=4

Step-by-step explanation:

The equation of a circle is (x-h)^2+(y-k)^2=r^2 where (h,k) is the center of the circle and r is the radius.

Since the center is (h,k)\rightarrow(-7,2), and the radius is r=2, then the equation of the circle graphed is (x-(-7))^2+(y-2)^2=2^2=(x+7)^2+(y-2)^2=4.

8 0
2 years ago
What is 2 times 4 i need a answer
ollegr [7]

Answer:

8

Step-by-step explanation:

7 0
3 years ago
I'm confused how do I simplify that??
Nina [5.8K]
2+3/5x-1-1/4x
2+3x-1/5-1-x/5
2+3/5x-1-x/5
1+3/5x-x/5
1+2/5x
8 0
2 years ago
Read 2 more answers
Derek has a white cube and a red cube.
cluponka [151]

Answer:

1/72

Step-by-step explanation:

Probability of getting a 4 on white cube is:

P(W) · P(4) = 1/2 × 1/6 = 1/12

P(R) · P(>4) = 1/2 × 2/6 = 1/6

multiply both probabilities:  1/12 × 1/6 = 1/72

3 0
2 years ago
Lease someone help me im so confused on how to find it.
LiRa [457]
The answer is D you simply get one point and move it 4 squares down and 6 squares to the right
5 0
3 years ago
Other questions:
  • One of the angles of a parallelogram is 36° greater then another one. Find the angles of the parallelogram.
    12·1 answer
  • which equation represents this sentence? one-half the sum of a number and four is three less than the quotient of five and the n
    9·2 answers
  • Need help writing a quadratic equation from a function given the graph, screenshot posted of the question
    14·1 answer
  • CAN SOMEONE HELP ME ANSWER THIS ​
    14·1 answer
  • How do you do number twenty four in the picture?
    10·1 answer
  • Why does the fact family for 81 and 9 only have two number sentences?
    10·1 answer
  • 6w-19+k when w=8 and k=2
    8·2 answers
  • A recipe requires one quarter cup of milk as a base and then, in addition, 1 cup of milk for every 4 cups of flour. Choose a lin
    15·1 answer
  • Which of these is a good conductor?<br> wood<br> silver<br> paper<br> air
    5·2 answers
  • Financial account and managerial accounting.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!