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Let X be the number of coffees ordered by customers at a certain café. The probability distribution for X is given by
The maximum number of drinks that can be ordered is 3.
Show that p=101​
Hence find
the average number of coffees ordered by a customer,
the probability that a customer will order 3 coffees given that she orders at least 1 coffee.
In the café, customers can play a fair dice game. The game consists of rolling a four sided die with face values q, 2,3 and 4. Let Y be the score obtained when the die is rolled. The probability distribution of Y is given in the following table.
It costs $1.75 to roll the dice, and players win their score in dollars ($).
Show that q satisfies q2−3q+1.25=0.
Find the value of r.
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The following table shows the distribution of a discrete random variable X.
Show that k=√2e​​.
Hence find E(X), giving your answer in the form a+lnb−lnc, where a,b,c∈Z.
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