Random Processes (AQA A-Level Further Maths): Quizzes

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Exponential Distribution
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What type of scenarios is the exponential distribution particularly useful for modelling?

Waiting times between random events

What does the 'memoryless' property of the exponential distribution mean?

Past waiting time doesn't affect future

What is the PDF of an exponential distribution with parameter λ\lambda?

f(x)=λeλxf(x) = \lambda e^{-\lambda x}, x>0x > 0

How does a larger value of λ\lambda affect the exponential distribution curve?

Steeper initial decline

What is the CDF of an exponential distribution with parameter λ\lambda?

F(x)=1eλxF(x) = 1 - e^{-\lambda x}, x>0x > 0

If XX follows an exponential distribution with parameter λ\lambda, what is E(X)E(X)?

1λ\frac{1}{\lambda}

If XX has PDF f(x)=λeλxf(x) = \lambda e^{-\lambda x}, what is Var(X)\text{Var}(X)?

1λ2\frac{1}{\lambda^2}

What is the relationship between mean and standard deviation for exponential distribution?

They are equal

If events occur at rate μ\mu per unit time, what is the exponential parameter for waiting time?

μ\mu

If XX has exponential distribution with λ=3\lambda = 3, what is P(X>2)P(X > 2)?

e6e^{-6}

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