A discrete probability distribution for a random variable X̅ is given. Use the given distributio

step 1 the probability that the random variable x is greater than or equal to 2 equals the probability

A discrete probability distribution for a random variable X̅...

A discrete probability distribution for a random variable $\bar{X}$ is given. Use the given distribution to find $(a)$ $P(X \geq 2)$ and $(b) E(X)$.
$$\begin{array}{c|ccccc}x_{i} & -2 & -1 & 0 & 1 & 2 \\\hline p_{i} & 0.1 & 0.2 & 0.4 & 0.2 & 0.1\end{array}$$

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Key Concepts

Expected Value Calculation

The expected value of a discrete random variable is a measure of the center of its distribution, calculated as the weighted average of all possible outcomes. Each outcome is multiplied by its corresponding probability, and the sum of these products gives the expected value, which represents the long-run average if the random experiment were repeated many times.

Tail Probability Calculation

Tail probability calculation involves summing the probabilities of outcomes that satisfy a given inequality. When a condition such as X being greater than or equal to a specified value is required, the probability is obtained by adding the probabilities corresponding to all outcomes meeting that condition.

Discrete Probability Distribution

A discrete probability distribution provides a list of all possible outcomes of a random variable along with the probabilities associated with each outcome. It allows one to understand the behavior of the random variable by outlining the chance of obtaining each specific value and ensuring that the total probability sums to one.

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