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APPLIED'PROBABILITY'AND'STATISTICS'FOR'ELECTRICAL'

ENGINEERS!!Chapter!3!

Examples

• Probability of pregnant woman having a boy

• Probability of getting a raise this year • Probability of passing this class

Example

OU’s place kicker has a certain probability p of missing a field goal. If we assume each kick is independent, then the random variable Z that is the number of kicks he makes before missing (including the missed kick) is what kind of random variable? What is it’s PMF?

Geometric Distribution Examples

Terminals on an on-line computer system are attached to a communication line to the central computer system. The probability that any terminal is ready to transmit is 0.95. Let X = number of terminals polled until the first ready terminal is located.

Geometric Distribution Examples

It is known that 10% of products on a production line are defective. Products are inspected until first defective is encountered. Let X = number of inspections to obtain first defective.

Geometric Distribution Examples

One percent of bits transmitted through a digital transmission are received in error. Bits are transmitted until the first error. Let X denote the number of bits transmitted until the first error.

What if a Bernoulli event happens many times?

We have seen this before: • Probability of getting 7 heads in 40 coin tosses

• Probability of observing 14 boys of 20 babies

• Probability of 8 people getting a raise of 30 employees

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What distribution is this?

Toss a coin repeatedly. Let X = number of tosses to first head.

What distribution is this?

Spin a “wheel of fortune” that has the numbers from 1-32 on it. The random variable is the number that gets chosen.

What distribution is this?

The number of passes a quarterback makes in a row.

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