[In MS Excel] In a bag, you placed papers containing the numbers 1, 2, 3, and...

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[In MS Excel] In a bag, you placed papers containing the numbers 1, 2, 3, and 4. The amount of papers for each number is uneven. The random variable X represents the outcome of a single draw and its probability distribution is shown below: X P(X) 1 0.10 2 3 4 0.20 0.15 0.55 o Find the expected value of X. (3 pts) o Interpret your obtained expected value in 2-3 sentences. (2 pts) [In MS Excel] A random variable M has this probability distribution: 0 Q 1 2 3 4 5 6 P(Q) 0.45 0.05 0.10 0.30 0.05 0.05 Find the expected value of M. (2 pts) Determine the variance and standard deviation. (3 pts) [In MS Excel] You went to play a game with your friend. In a standard deck, you will take turns in drawing a card (with replacement). He will pay you Php 100 for every number card and Php 200 for every ace that you will draw. However, you need to pay him Php 300 for every face card that he will draw. o If you continue to play the game, how much do you expect to win or lose? (2 pts) o Determine the variance and standard deviation of your gain or lose. (3 pts) [In MS Excel] In a bag, you placed papers containing the numbers 1, 2, 3, and 4. The amount of papers for each number is uneven. The random variable X represents the outcome of a single draw and its probability distribution is shown below: X P(X) 1 0.10 2 3 4 0.20 0.15 0.55 o Find the expected value of X. (3 pts) o Interpret your obtained expected value in 2-3 sentences. (2 pts) [In MS Excel] A random variable M has this probability distribution: 0 Q 1 2 3 4 5 6 P(Q) 0.45 0.05 0.10 0.30 0.05 0.05 Find the expected value of M. (2 pts) Determine the variance and standard deviation. (3 pts) [In MS Excel] You went to play a game with your friend. In a standard deck, you will take turns in drawing a card (with replacement). He will pay you Php 100 for every number card and Php 200 for every ace that you will draw. However, you need to pay him Php 300 for every face card that he will draw. o If you continue to play the game, how much do you expect to win or lose? (2 pts) o Determine the variance and standard deviation of your gain or lose. (3 pts)