$X$ is a discrete random variable with possible values $\{-3,-1,0,1,5\}$. The expected value of $X$ is?

Question

BlackTom AI · Accepted Answer

Consider the question: an X that is discrete with possible values {-3, -1, 0, 1, 5}. The prompt asks for the expected value E(X).

Option: 'a. We cannot compute E(X) because we do not know the probability of each outcome.'

First, recall the definition: the expected value E(X) = sum over all x of x * P(X = x). This requires knowing the probability distribution (the probabilities assigned to -3, -1, 0, 1, and 5).

If the probabilities P(X = -3), P(X = -1), P(X = 0), P(X = 1), and P(X = 5) are not provided, then indeed we cannot compute a numeric value for E(X). Without those probabilities, the sum is undefined.

However, consider potential special cases to understand the nuance:
- If the problem had specified a particular distribution (e.g., uniform distribution over the five values), we could compute E(X) by plugging in those probabilities into the formula. For example, under a uniform distribution with P(X = x) = 1/5 for each x, E(X) would be (-3 - 1 + 0 + 1 + 5)/5 = 2/5 = 0.4.
- If the problem provided some probabilities (even if not all), we could compute a partial contribution to E(X) for the known values and note that the unknowns prevent a full calculation.

But given only the set of possible values and no probabilities, the statement in option a correctly identifies the obstacle: the expected value cannot be computed numerically without the probability distribution.

In terms of common misunderstandings: some students might think you can compute E(X) from the values alone, forgetting that the weights (probabilities) are essential. Others might assume a default like equal likelihood for all outcomes; that assumption is not stated, so it would be speculative.

Overall, option a is accurate for the information provided, because E(X) depends on the probabilities assigned to each outcome, which are not given here.

ETC2410 - ETC5241 - BEX2410 - S2 2025 Tutorial 3: Part A Quiz

\(X\) is a discrete random variable with possible values \(\{-3,-1,0,1,5\}\). The expected value of \(X\) is?

查看解析

登录即可查看完整答案

类似问题

[continues question 6] Suppose that a testing company offers to test the house for Radon gas contamination before deciding whether or not to buy and rent the house. The cost of the test is 10. Then,

Let p=0.23 and q=0.74. What is E(Y)?

A system integration carries a 35% chance of requiring $600,000 rework. What is the Expected Monetary Value (EMV) of this risk?

Let s=0.25. What is the expected value of UC-UM?

Let r=0.55, c=2.1 and m=1.1. Suppose that UC and UM are not independent. What is the expected value of the point spread in the UBC game? Enter "999" if there is insufficient information to answer.

Suppose q=0.27. Find the expected value of X.

Suppose p=0.15. What is E(W)? (Hint: What are the possible values of W, and what are the associated probabilities?)

If p = 0.3, what is the expected number of friend requests per day? (Hint: Compute the probability of P(X=n) for each n=0,1,2,3. Then apply the expected value formula.)

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单