IDNStudy.com, kung saan ang iyong mga tanong ay natutugunan ng mga eksperto. Alamin ang mga detalyadong sagot sa iyong mga tanong mula sa aming malawak na kaalaman sa mga eksperto.
Answer:
Step-by-step explanation:
To find the Expected Gain, we need to multiply each prize amount by the probability of winning that prize, and then sum up all the products.
Let's calculate the Expected Gain:
E(x) = (1/200) * 5000 + (5/200) * 3000 + (8/200) * 1000 + (10/200) * 500
E(x) = 25 + 75 + 40 + 25
E(x) = 165
So, if you buy one ticket, your expected gain is Php 165.
Next, to find the Variance Gain, we need to calculate the squared difference between each prize amount and the expected gain, multiply it by the probability of winning that prize, and then sum up all the products.
Let's calculate the Variance Gain:
V(x) = [(5000 - 165)^2 * (1/200)] + [(3000 - 165)^2 * (5/200)] + [(1000 - 165)^2 * (8/200)] + [(500 - 165)^2 * (10/200)]
V(x) = [4835^2 * (1/200)] + [2835^2 * (5/200)] + [835^2 * (8/200)] + [335^2 * (10/200)]
V(x) = [23337422.5] + [3368662.5] + [58587.5] + [28058.75]
V(x) = 27095030.75
Therefore, the Variance Gain is Php 27,095.03.
So, your expected gain is Php 165, and your Variance Gain is Php 27,095.03 if you buy one ticket