X and Y are two random variables that follow a defined joint probability distribution. We know that E[XY]=E[X]E[Y] Pr(X=1)=0 3, and Pr(Y=4)=0 2 Please identify all correct statements below

The joint probability Pr((=1 and Y=4) = 0.3’0.2 = 0.06

X and Y are not linearly correlated

X and Y are independent.

There is no curvilinear relationship between x and Y

All of the above statements are correct.

The weekly demand for TVs at Challenger Clementi is normally distributed with a mean of 400 and a standard deviation of 100. Each time an order for TVs is placed, it arrives exactly 4 weeks later. That is, TV orders have a 4-week lead time. Challenger Clementi doesn’t want to run out of TVs during any more than 1% of all lead times. Please identify all correct statements below.

The standard deviation of the 4•week demand is 200.

The standard deviation of the 4•week demand is 400.

When the inventory level arrives at 2065 or 2066, Challenger Clement must place a TV order.

When the inventory level arrives at 2530 or 2531, Challenger Clement must place a TV order.

None of the above statements is correct.

The Sentosa virus has caused a slowdown in the economy. Both the property and stock markets have tumbled quite a bit. Alex is a real estate investor and believes that now is the best time to buy properties for investment. He has recently bought 10 identical units in the newly developed FloraLife Condo. with a unit price of 51.8M. He plans to sell the 10 units five years later and expects the unit selling price to follow a normal distribution with a mean of 82.2M and a standard deviation of 50.6M. Alex needs to pay 2% of the selling price to his agent for selling the units.

what is the expected profit? Your answer is 1 M

What is the standard deviation of the profit? Your answer is 2 M

What is the probability that Alex will make a profit out of it?

According to data from 115 customs, on January first, 2016 between 12 pm to 6 pm, there were 326 travelers arriving at Waterloo airport in Iowa. Among them. 10 persons were classified as having immigrant intent. After collecting more data on different days, the airport management arrived at a good estimate of the daily number of travelers with immigrant intent. Explicitly, on average there are 24 travelers with immigrant intent per day at this airport. Assume this trend continued in the year 2017 and every traveler was independent of each other in a probabilistic sense. Just observe travelers entering the same airport. Please pick up the correct probability statements below.

The probability that there are less than 30 travelers with immigrant intent on 2017 February 2 and 3 is 4.9032E-11

On 2017 February 1 afternoon between 12 pm to 2 pm, the probability that no one has immigrant intent among 40 travelers is 0.2876.

The probability that there are at most 50 travelers with immigrant intent on 2017 February 2 and 3 is 0.0002155.

On 2017 February 1 afternoon between 12 pm to 2 pm, the probability that no one has immigrant intent among 40 travelers is 0.1353.

The probability that there are less than 30 travelers with immigrant intent on 2017 February 2 and 3 is 0.002178.

Which of the following statements are incorrect,

Let X be a discrete random variable. Moreover. Y is another random variable such that Pr(Y = 10) = 1 Then. we know Cov(X. Y) > 0

Similar to variance. covariance is always non-negative.

The bigger the correlation is. the stronger the relationship between two random variables is.

Correlation between two random variables is always between -1.0 and 1 0 inclusive

Scatter plots are used to explain whether two random variables are positively correlated or negatively correlated.

In a given basket of durians from the same durian tree. suppose that the weight of each durian follows a normal distribution with a mean of 1.5kg and a standard deviation of 0.2kg. What is the probability that two durians from that basket have a combined weight of more than 3.2kg?

Hard to tell

0.48

0.56

0.24

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