The Exponential Distribution and Exponential Random Variables | Probability Theory

[@statisticstutoring1911]

Best explanations of math concepts on youtube. Please do more advanced math. Real analysis and abstract algebra! Thanks.

[@beefandpotatoes6525]

after many years I understood why in an exponentially distributed continues random variable probability of x >= a is e ^ (- ax ). Thank you man.

[@WrathofMath]

So glad it helped!

[@jeffreya.faulkner8367]

I like to think of lambda as the rate parameter and mu as the "wait" parameter. Lambda = 1/5 would be one call per five minutes; mu = 5/1 would be five minutes per one call.

[@beefandpotatoes6525]

Thank you Jeffrey. U put it in perspective.

[@abhishekroy3514]

Thanks for making the video. It really helps me to understand the basics in actuarial field.

[@WrathofMath]

You're very welcome, thanks for watching! And you're pursuing a career as an actuary? That's awesome! I'll definitely make more videos you'll be interested in. I'm an actuarial analyst so I like to think this stuff is my specialty!

[@abhishekroy3514]

@@WrathofMath Love to see your lovely response. Currently I am preparing for CS1 exam from IFOA. Thanks for creating "Wrath of Math"

[@WrathofMath]

Good luck! I wasn't familiar with the IFOA until you mentioned it! I have been on the SOA exam path, but the IFOA is a UK group, so that is why I have not heard of it, since I dwell here in the US! I'll definitely take a look at some of the CS1 Exam curriculum and see if I get any good lesson ideas from it! And you're very welcome! It is my deepest pleasure to run Wrath of Math, and I have to thank you and everyone else for watching, there'd be no point to making the lessons if they didn't help anyone. The support of you all keeps me motivated and gives me the energy to blab to my microphone about probability at ten at night! And I'll be doing lessons in front of a whiteboard soon as well, I can't wait :)

[@James08091980]

Great recap. It really helped me piece a bunch of stuff together

[@WrathofMath]

So glad it helped, thanks a lot for watching!

[@muhammadbinuzair2101]

Thank you so so much

[@AnoushkaFarrelly]

I know this was published three years ago but could you do a video about poisson to exponential distributions

[@Shaan_Suri]

Whats the difference between a probability density function and probability mass function ?

[@fortunatesadiq9662]

why is it P(X

[@nouramohammad3720]

i have a question , i can't solve Let X ~ Exponential (lambda), and Y=aX, where a is a positive real number. Show that Y~ Exponential (lambda/a).

[@WrathofMath]

Thanks for watching and good question! To show Y is exponential with mean a/lambda we need to show that Y has the probability density function of an exponential with parameter lambda/a. I'll do a lesson on how to prove that soon!

[@gauravchaudhari3843]

thank you

[@WrathofMath]

My pleasure! Thanks for watching, Gaurav!

[@miracleodion8401]

Your video on exponential distribution is helpful.i need your help on this particular question Suppose that the time between emergency calls in a fire station follows the exponential distribution with an average rate of 2 calls per day.what is the probability that the firemen are not called in 3 days?

[@omarsaad6543]

Hello Sir, 1. A system consists of three processors and four peripheral units. In each of these cases find the reliability of the system if the processor lifetimes are exponential random variable with mean 10 and the peripheral lifetimes are exponential random variable with mean 15. a) The system is functioning as long as one processor and one peripheral are functioning. b) The system is functioning as long as two processors and two peripherals are functioning. Any suggestions pls?

[@zack_120]

5:40 - are you joking or serious: σ=1/λ=E(x), meaning μ=σ (!?) since μ=1/λ.

[@reidchave4054]

He is serious! The neat property of exponential random variables is that the standard deviation is always equal to the expected value. This means that 0, and all values up to 2σ, are within σ distance of the expected value (μ), or to put it more simply, that every time you wait the expected value of time (μ) AFTER the expected value before observing the event, you are one more standard deviation beyond the mean.

[@andreaaa2736]

😍😍

[@WrathofMath]

Thanks for watching!

[@andreaaa2736]

@@WrathofMath your videos help me a lot 😍 It's clear and easy to understand