The first or second answer
Answer:
1/4 or 25%
Step-by-step explanation:
there are four different suits in total in a card deck. There is an even amount of each one (Diamonds, Spades, Clubs, Hearts). Therefore, you have a 1 in four chance- or a 25% chance of drawing a diamond.
Answer:
If it's: Find the value of the constant.
=
5
f
Step-by-step explanation:
Answer:

And we can calculate this with the complement rule like this:

And using the cdf we got:
![P(X>2) = 1- [1- e^{-\lambda x}] = e^{-\lambda x} = e^{-\frac{1}{2.725} *2}= 0.480](https://tex.z-dn.net/?f=%20P%28X%3E2%29%20%3D%201-%20%5B1-%20e%5E%7B-%5Clambda%20x%7D%5D%20%3D%20e%5E%7B-%5Clambda%20x%7D%20%3D%20e%5E%7B-%5Cfrac%7B1%7D%7B2.725%7D%20%2A2%7D%3D%200.480)
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:
And 0 for other case. Let X the random variable of interest:

Solution to the problem
We want to calculate this probability:

And we can calculate this with the complement rule like this:

And using the cdf we got:
![P(X>2) = 1- [1- e^{-\lambda x}] = e^{-\lambda x} = e^{-\frac{1}{2.725} *2}= 0.480](https://tex.z-dn.net/?f=%20P%28X%3E2%29%20%3D%201-%20%5B1-%20e%5E%7B-%5Clambda%20x%7D%5D%20%3D%20e%5E%7B-%5Clambda%20x%7D%20%3D%20e%5E%7B-%5Cfrac%7B1%7D%7B2.725%7D%20%2A2%7D%3D%200.480)