[4] Approximate the following binomial probabilities by the use of normal approximation (n = 50, p = 0.3). Remember to use a continuity correction. P(x = 18) P(x ≥ 15) P(x ≤ 12) P(12 ≤ x ≤ 18)

I don't understand this question as well too?

If a continuous random process has a probability density function f(x) = a + bx, for 0 < x < 5, where a and b are constants, and P(X > 3) = 0.3 Determine:

1. The values of a and b.
2. The cumulative distribution function F(x)
3. P(X < 2)
4. P(2 < X < 4)

In a system of three particles, each particle has three quantum states. The energies of these situations are 0.3? and 5?, respectively. Write the partition functions of the particles that meet the following conditions.
a) If the particles are distinguishable
b) Particles comply with Bose-Enistein statistics
c) If the particles match Fermi-Dirac statistics

The Magazine Mass Marketing Company has received 18 entries in its latest sweepstakes. They know that the probability of receiving a magazine subscription order with an entry form is 0.3. What is the probability that more than 3 of the entry forms will include an order? Round your answer to four decimal places.

If a continuous random process has a probability density function f(x) = a + bx, for 0 < x < 5, where a and b are constants, and P(X > 3) = 0.3 Determine:

1. The values of a and b.
2. The cumulative distribution function F(x)
3. P(X < 2)
4. P(2 < X < 4)

Joe can choose to take the freeway or not for going to work.

There is a 0.4 chance for him to take the freeway. If he chooses freeway, Joe is late to work with probability 0.3; if he avoids the freeway, he is late

with probability 0.1

Given that Joe was early, what is the probability that he took freeway?

Volkswagen in Russia In the mid-2000s, Volkswagen announced that it would invest directly in automobile production in Russia. The decision to invest was driven by a number of factors. Russia’s economy was growing rapidly at the time and living standards were rising, while the level of car ownership per capita was still low by European standards. This suggested that demand for cars would grow rapidly going forward. Indeed, forecasts predicted that by 2020, Russia would surpass Germany to become the largest car market in Europe. Moreover, Volkswagen’s global rivals, including most notably Toyota, General Motors, and Ford, were also investing in production facilities in Russia, so Volkswagen felt that it had to make direct investments in order to avoid being preempted by its rivals. The Russian government also createdPage 238 incentives for carmakers to invest directly in Russian production facilities, allowing them to avoid import tariffs and a punitive tax on imports of parts if they produced at least 25,000 cars in the country. In 2011, the government announced that it would keep tariffs on imported components at 0.3 percent if a foreign automaker built at least 300,000 in the country by 2020 and produced 60 percent of the value of the car locally. Spurred on by such incentives, in 2007 Volkswagen opened a plant in Kaluga, 160 miles southwest of Moscow, to build some of its VW and Skoda car brands. The plant was projected to have a peak capacity of 150,000 units a year and employ 3,000 people. Initially all vehicles at the plant were assembled from semi-knocked-down kits imported from Germany. In October 2009, however, the plant launched full-scale production, including welding and painting of vehicles. In October 2011, Volkswagen announced that, together with a local partner, GAZ Group, it would open a second plant near St. Petersburg, as it strove to reach the 300,000 units of local production by 2020. In 2013, Volkswagen made an additional investment in Kaluga when it pledged 300 million euros to build an engine plant near to its assembly operation. The engine plant opened in September 2015. All told, by this point Volkswagen had invested over $1 billion in production in Russia. General Motors and Toyota had also announced investments of over $1 billion to boost Russian production up to 300,000 units by 2020, and Fiat had indicated that it would make investments to bring its Russian production up to 300,000 as well. In total, foreign carmakers had invested over $5 billion in Russian assembly operations by 2014. Meanwhile, analysts continued to predict that the Russian car market would grow at a healthy pace and exceed that of Germany by 2020. In 2014, however, the market took a sharp turn for the worse. Russia is a major oil producer. Since the mid-2000s, much of the country’s economic growth had been powered by high oil prices. In the second half of 2014, however, global oil prices started to fall rapidly as increased production in America and weak demand in China conspired to create a global glut of oil. By early 2016, oil prices had fallen 80 percent from their peak. To make matters worse, following hard on the heals of its hostile takeover of the Crimea region from Ukraine, Russia had become embroiled in a smoldering civil war in eastern Ukraine. Western nations responded to what they perceived as Russian aggression by imposing sanctions on Russia. Hit by these twin blows, the Russian economy weakened significantly in 2014 and 2015, and the ruble declined precipitously, losing 50 percent of its value against the U.S. dollar. Suddenly the bright hopes that foreign automakers had for the Russian market seemed to be tarnished. Faced with falling demand, Volkswagen cut production at its Kaluga plant to 120,000 vehicles from a planned 150,000. With the new engine plant scheduled to come on line and no resolution to Russia’s economic crisis insight, Volkswagen’s excess capacity problem may get worse. Looking forward, Volkswagen has to decide whether to keep investing in Russia in order to hit the magic 300,000 local output figure by 2020 or to pull back from a market whose future suddenly looks highly uncertain. At this point, it looks as if Volkswagen is staying the course. In late 2015, a Volkswagen board member noted that “We need to continue to strengthen our partnership (in Russia) despite the current situation”.* Sources: Sarah Sloat, “Volkswagen to Halt Production at Russian Plant for 10 Days,” The Wall Street Journal, September 7, 2014; Clare Nuttall, “Foreign Car Firms Invest Heavily in Russia,” The Telegraph, April 28, 2011; Staff reporter, “Volkswagen Russia Shows the Way,” Automotive Supply Chain, July 2, 2013; Staff reporter, “Volkswagen Slashes Car Production at Russian Plat,” Reuters, September 7, 2014.

Question: Volkswagen has signaled that it is going to stay the course in Russia, despite current political and economic headwinds. Why do you think it made this decision? What are the pros and cons of this decision?

How can I make my own function for rbinom(n, size, prob) in R.

So, basically I want to build my own rbinom function that gives me the same result as rbinom that's built in R software.

Write a 2-page overview of the project and your participation in the User interface of a new smartwatch built specifically for athletes... Clearly delineate your role and responsibilities.

Discuss what you have learned about Human-Computer Interaction

#No plagiarism, please

Discuss supply side economics in the context of a negative temporary supply shock of the 1970s a. what arte the primary supply side policies? b in your opinion does President Trump have supply side economics built into his economic platform?