题目
题目

MTH5210 - S1 2025 Quiz1

单项选择题

A fair coin is tossed 2 times. The random variable X is the number of Heads in two tosses and Y is the number of Heads on the first toss.The conditional expectation E(X|Y) is given by

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思路分析
To find E(X | Y), we consider the two possible values of Y, which represents the outcome of the first toss. - If Y = 0 (the first toss is Tails): then the number of Heads X in t......Login to view full explanation

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类似问题

According to an expert, the inflation rate and the cash rate (the interest rate set by the Reserve Bank of Australia) in Australia in the next quarter is governed by the following joint probability density function: \[ \begin{matrix} \text{cash rate } \downarrow \diagdown \text{inflation rate } \longrightarrow & 1.00\% & 1.25\% & 1.50\% \\ \hline 0.05\% & 0.06 & 0.10 & 0.00 \\ 0.10\% & 0.04 & 0.50 & 0.10 \\ 0.25\% & 0.00 & 0.10 & 0.10\end{matrix} \] According to this expert, what is the expected value of the inflation rate conditional on cash rate staying at \(0.10\%\) next quarter? Do all calculations to the highest precision and then round your final answer to two decimal points and enter it in percentage points but without the % sign.

Question at position 8 Consider the following joint distribution of X and Y. [table] X | Y | P(X=x,Y=y) 3 | 10 | 0.18 3 | 15 | 0.12 3 | 18 | 0.04 4 | 10 | 0.15 4 | 15 | 0.19 4 | 23 | 0.01 5 | 15 | 0.07 5 | 18 | 0.11 5 | 23 | 0.13 [/table] What is E(Y|X=4)E(Y|X=4)? Round your answer to 3 decimal places.AnswerConsider the following joint distribution of X and Y. [table] X | Y | P(X=x,Y=y) 3 | 10 | 0.18 3 | 15 | 0.12 3 | 18 | 0.04 4 | 10 | 0.15 4 | 15 | 0.19 4 | 23 | 0.01 5 | 15 | 0.07 5 | 18 | 0.11 5 | 23 | 0.13 [/table] What is E(Y|X=4)E(Y|X=4)? Round your answer to 3 decimal places.[input]BlackTom题目解析

Question at position 2 Consider two variables, Y and X. Y is a continuous random variable, while X is a discrete random variable that takes only values 0 and 1. In particular, P(X=0)=P(X=1)=0.5P(X=0) = P(X=1) = 0.5. Suppose that you know E(Y)=4.25E(Y) = 4.25. If E(Y|X=0)=5E(Y|X=0) = 5, what is E(Y|X=1)E(Y|X=1)? Enter your answer as an exact number.AnswerConsider two variables, Y and X. Y is a continuous random variable, while X is a discrete random variable that takes only values 0 and 1. In particular, P(X=0)=P(X=1)=0.5P(X=0) = P(X=1) = 0.5. Suppose that you know E(Y)=4.25E(Y) = 4.25. If E(Y|X=0)=5E(Y|X=0) = 5, what is E(Y|X=1)E(Y|X=1)? Enter your answer as an exact number.[input]BlackTom题目解析

Following the question above, what is the conditional expectation of 𝑋 1 given 𝑋 2 = 1 ?

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