4. Continuous RVs

4. Continuous RVs

Probability density function

Uniform

• Parameter:

• PDF:

• CDF:

• Mean:

• Variance:

LOTUS

Normal(Gaussian)

• Parameter:

• PDF:

• Mean:

• Variance:

Standard Normal

• , then

LOTUS

Exponential

• Parameter:

• PDF:

• CDF:

• Mean:

• Variance:

Min

Memoryless property

• successive buses arrives at 10 min, uniformly random time

• wait for the next bus:

• not yet arrived after 6 min, probability at least 3 more min:

• successive buses arrives at mean 10 min, with exponential distribution

• wait for the next bus:

Clerk

• 2 clerks, 2 customers + new customer come in now

• last of the 3 customers to be done being served:

• expected time spent waiting in line:

• expected time spent being served:

Used car

• sell to the first person to offer at least $15000

• offers exponential with mean $10000:

Poisson process

• How many emails will arrive per hour?
• Number of arrivals in an interval of length 1:

• How long does it take until the first email arrive?
• Times btw arrivals are i.i.d.:

• 3 people start at 1, takes time: