A car has five traffic lights on its route. Independently of other traffic lights, each traffic light turns red as the car approaches the light (and thus forces the car to stop at the light) with a probability of 0.4. a Let K he a random variable that denotes the number of lights at which the car stops with parameters (5,0.4). What is the PMF of K? b. What is the probability that the car stops at exactly two lights? c. What is the probability that the car stops at more than two lights? d.What is the expected value and the variance of K?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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Assignment 3.pdf
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SCST 310
Assignment# 3
Chapter# 4
Question# 1:
A car has five traffic lights on its route. Independently of other traffic lights, each traffic light turns red as the
car approaches the light (and thus forces the car to stop at the light) with a probability of 0.4.
a. Let K he a random variable that denotes the number of lights at which the car stops
with parameters (5,0.4), What is the PMF of K?
b. What is the probability that the car stops at exactly two lights?
c. What is the probability that the car stops at more than two lights?
d. What is the expected value and the variance of K
Question# 2:
The number of phone calls that arrive at a secretary's desk has a Poisson distribution with a mean of 4 per hour.
a What is the probability that no phone calls arrive within hour?
b. What is the prohability that more than 2 calls arrive within a given hour?
e. What is the prohability that exactly three calls arrive within a given hour?
Question# 3
The lifetime X of a system in weeks is given by the following PDF:
0.25 e-a2s x
fklx] =
x< 0
a. What is the expected value of X?
b. What is the CDF of X?
e. What is the variance of X?
d. What is the probability that the system will not fail within two weeks?
SCST 310
Assignment# 3
Chapter# 4
Question# 4:
A random variable X is uniformly distributed between 3 and 15. Find the following:
a The expected value of X.
b. The variance of X.
c. The probability that X lies between 5 and 10.
d. The probability that X is less than
Question# 5:
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